Oregon State basketball player Destiny Slocum has opted to enter the transfer portal for her final season of eligibility. Slocum, a 5-foot-7 guard, averaged a team-best 14.9 points and had 4.7 assists a game this past season with the Beavers, who finished the season ranked No. 14 with a 23-9 record. In a statement released by the university on Thursday, Slocum thanked everyone who supported her in the decision.

Since the day she stepped on campus, Satou Sabally's game has turned heads — and for good reason. She's had many memorable moments in a Duck uniform, including a standout performance against the USA Women in Nov. 2019, a monster game against Cal in Jan. 2020 and a career performance in Pullman in Jan. 2019.

Pac-12 Networks' Mike Yam interviews former Oregon State guard Sydney Wiese to hear how she's recovering from contracting COVID-19. Wiese recounts her recent travel and how she's been lifted up by steadfast support from friends, family and fellow WNBA players. See more from Wiese during "Pac-12 Playlist" on Monday, April 6 at 7 p.m. PT/ 8 p.m. MT on Pac-12 Network.

Maori Davenport, who drew national attention over an eligibility dispute during her senior year of high school, is transferring to Georgia after playing sparingly in her lone season at Rutgers. Lady Bulldogs coach Joni Taylor announced Davenport's decision Wednesday. The 6-foot-4 center from Troy, Alabama will have to sit out a season under NCAA transfer rules before she is eligible to join Georgia in 2021-22.

Baylor has signed a transfer point guard for the third year in a row, and this one can play multiple seasons with the Lady Bears. Jaden Owens is transferring from UCLA after signing a national letter of intent with Baylor, which had graduate transfers at point guard each of the past two seasons. The Texas native just completed her freshman season with the Bruins and has three seasons of eligibility remaining.

The Pac-12 Student-Athlete Advisory Committee voted to award the Oregon State women’s basketball team with the Pac-12 Sportsmanship Award for the 2019-20 season, honoring their character and sportsmanship before a rivalry game against Oregon in Jan. 2020 -- the day Kobe Bryant, his daughter, Gigi, and seven others passed away in a helicopter crash in Southern California. In the above video, Aleah Goodman and Madison Washington share how the teams came together as one in a circle of prayer before the game.

On the day Kobe Bryant suddenly passed away, the Beavers embraced their rivals at midcourt in a moment of strength to support the Ducks, many of whom had personal connections to Bryant and his daughter, Gigi. For this, Oregon State is the 2020 recipient of the Pac-12 Sportsmanship Award.

The process is based on the U.S. three-phase federal guidelines for easing social distancing and re-opening non-essential businesses.

Anatoli Juditsky, Arkadi Nemirovski.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 458--502.

Abstract:
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable non linear in observations “polyhedral” estimate along with computation-friendly techniques for its design and risk analysis. We demonstrate that under favorable circumstances the resulting estimate is provably near-optimal in the minimax sense, the “favorable circumstances” being less restrictive than the weakest known so far assumptions ensuring near-optimality of estimates which are linear in observations.

Daren Wang, Yi Yu, Alessandro Rinaldo.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1917--1961.

Abstract:
The problem of univariate mean change point detection and localization based on a sequence of $n$ independent observations with piecewise constant means has been intensively studied for more than half century, and serves as a blueprint for change point problems in more complex settings. We provide a complete characterization of this classical problem in a general framework in which the upper bound $sigma ^{2}$ on the noise variance, the minimal spacing $Delta $ between two consecutive change points and the minimal magnitude $kappa $ of the changes, are allowed to vary with $n$. We first show that consistent localization of the change points is impossible in the low signal-to-noise ratio regime $frac{kappa sqrt{Delta }}{sigma }preceq sqrt{log (n)}$. In contrast, when $frac{kappa sqrt{Delta }}{sigma }$ diverges with $n$ at the rate of at least $sqrt{log (n)}$, we demonstrate that two computationally-efficient change point estimators, one based on the solution to an $ell _{0}$-penalized least squares problem and the other on the popular wild binary segmentation algorithm, are both consistent and achieve a localization rate of the order $frac{sigma ^{2}}{kappa ^{2}}log (n)$. We further show that such rate is minimax optimal, up to a $log (n)$ term.

Assaf Rabinowicz, Saharon Rosset.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 272--301.

Abstract:
Common model selection criteria, such as $AIC$ and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error does not represent the relevant prediction error. In this paper new prediction error estimators, $tAI$ and $Loss(w_{t})$ are introduced. These estimators generalize previous error estimators, however are also applicable for assessing prediction error in cases involving interpolation and extrapolation. Based on these prediction error estimators, two model selection criteria with the same spirit as $AIC$ and Mallow’s $C_{p}$ are suggested. The advantages of our suggested methods are demonstrated in a simulation and a real data analysis of studies involving interpolation and extrapolation in linear mixed model and Gaussian process regression.

Patrick L. Combettes, Christian L. Müller.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 207--238.

Abstract:
We introduce a flexible optimization model for maximum likelihood-type estimation (M-estimation) that encompasses and generalizes a large class of existing statistical models, including Huber’s concomitant M-estimator, Owen’s Huber/Berhu concomitant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as various regularizers are instances of perspective functions, a construction that extends a convex function to a jointly convex one in terms of an additional scale variable. These nonsmooth functions are shown to be amenable to proximal analysis, which leads to principled and provably convergent optimization algorithms via proximal splitting. We derive novel proximity operators for several perspective functions of interest via a geometrical approach based on duality. We then devise a new proximal splitting algorithm to solve the proposed M-estimation problem and establish the convergence of both the scale and regression iterates it produces to a solution. Numerical experiments on synthetic and real-world data illustrate the broad applicability of the proposed framework.

Ben Jones, Andreas Artemiou, Bing Li.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1--23.

Abstract:
We give a probabilistic analysis of a phenomenon in statistics which, until recently, has not received a convincing explanation. This phenomenon is that the leading principal components tend to possess more predictive power for a response variable than lower-ranking ones despite the procedure being unsupervised. Our result, in its most general form, shows that the phenomenon goes far beyond the context of linear regression and classical principal components — if an arbitrary distribution for the predictor $X$ and an arbitrary conditional distribution for $Yvert X$ are chosen then any measureable function $g(Y)$, subject to a mild condition, tends to be more correlated with the higher-ranking kernel principal components than with the lower-ranking ones. The “arbitrariness” is formulated in terms of unitary invariance then the tendency is explicitly quantified by exploring how unitary invariance relates to the Cauchy distribution. The most general results, for technical reasons, are shown for the case where the kernel space is finite dimensional. The occurency of this tendency in real world databases is also investigated to show that our results are consistent with observation.

Wei Li, Subhashis Ghosal.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1707--1743.

Abstract:
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional characterization of multivariate data. There have been some recent theoretical studies of filaments in the nonparametric kernel density estimation context. This paper supplements the current literature in two ways. First, we provide a Bayesian approach to the filament estimation in regression context and study the posterior contraction rates using a finite random series of B-splines basis. Compared with the kernel-estimation method, this has a theoretical advantage as the bias can be better controlled when the function is smoother, which allows obtaining better rates. Assuming that $f:mathbb{R}^{2}mapsto mathbb{R}$ belongs to an isotropic Hölder class of order $alpha geq 4$, with the optimal choice of smoothing parameters, the posterior contraction rates for the filament points on some appropriately defined integral curves and for the Hausdorff distance of the filament are both $(n/log n)^{(2-alpha )/(2(1+alpha ))}$. Secondly, we provide a way to construct a credible set with sufficient frequentist coverage for the filaments. We demonstrate the success of our proposed method in simulations and one application to earthquake data.

Aurélie Fischer, Dominique Picard.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1648--1689.

Abstract:
In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a maximum likelihood method. We are interested in how dimension reduction can affect the performance of the method. We provide an estimator of the change-point that has a minimax rate of convergence, up to a logarithmic factor. The minimax rate is in fact composed of a fast rate —dimension-invariant— and a slow rate —increasing with the dimension. Moreover, it is proved that considering the case of sparse data, with a Sobolev regularity, there is a bound on the separation of the regimes above which there exists an optimal choice of dimension reduction, leading to the fast rate of estimation. We propose an adaptive dimension reduction procedure based on Lepski’s method and show that the resulting estimator attains the fast rate of convergence. Our results are then illustrated by a simulation study. In particular, practical strategies are suggested to perform dimension reduction.

Yuling Yan, Bret Hanlon, Sebastien Roch, Karl Rohe.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1577--1610.

Abstract:
Respondent-driven sampling (RDS) collects a sample of individuals in a networked population by incentivizing the sampled individuals to refer their contacts into the sample. This iterative process is initialized from some seed node(s). Sometimes, this selection creates a large amount of seed bias. Other times, the seed bias is small. This paper gains a deeper understanding of this bias by characterizing its effect on the limiting distribution of various RDS estimators. Using classical tools and results from multi-type branching processes [12], we show that the seed bias is negligible for the Generalized Least Squares (GLS) estimator and non-negligible for both the inverse probability weighted and Volz-Heckathorn (VH) estimators. In particular, we show that (i) above a critical threshold, VH converge to a non-trivial mixture distribution, where the mixture component depends on the seed node, and the mixture distribution is possibly multi-modal. Moreover, (ii) GLS converges to a Gaussian distribution independent of the seed node, under a certain condition on the Markov process. Numerical experiments with both simulated data and empirical social networks suggest that these results appear to hold beyond the Markov conditions of the theorems.

Christophe A. N. Biscio, Nicolas Chenavier, Christian Hirsch, Anne Marie Svane.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1024--1074.

Abstract:
We introduce tests for the goodness of fit of point patterns via methods from topological data analysis. More precisely, the persistent Betti numbers give rise to a bivariate functional summary statistic for observed point patterns that is asymptotically Gaussian in large observation windows. We analyze the power of tests derived from this statistic on simulated point patterns and compare its performance with global envelope tests. Finally, we apply the tests to a point pattern from an application context in neuroscience. As the main methodological contribution, we derive sufficient conditions for a functional central limit theorem on bounded persistent Betti numbers of point processes with exponential decay of correlations.

Daniel Rudolf, Björn Sprungk.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 857--889.

Abstract:
A classical approach for approximating expectations of functions w.r.t. partially known distributions is to compute the average of function values along a trajectory of a Metropolis–Hastings (MH) Markov chain. A key part in the MH algorithm is a suitable acceptance/rejection of a proposed state, which ensures the correct stationary distribution of the resulting Markov chain. However, the rejection of proposals causes highly correlated samples. In particular, when a state is rejected it is not taken any further into account. In contrast to that we consider a MH importance sampling estimator which explicitly incorporates all proposed states generated by the MH algorithm. The estimator satisfies a strong law of large numbers as well as a central limit theorem, and, in addition to that, we provide an explicit mean squared error bound. Remarkably, the asymptotic variance of the MH importance sampling estimator does not involve any correlation term in contrast to its classical counterpart. Moreover, although the analyzed estimator uses the same amount of information as the classical MH estimator, it can outperform the latter in scenarios of moderate dimensions as indicated by numerical experiments.

Ery Arias-Castro, Rong Huang, Nicolas Verzelen.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 702--730.

Abstract:
In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main component. We first look at this problem in the context of a normal mixture model. In essence, the situation reduces to a univariate setting where the effect is a decrease in variance. In particular, a higher criticism test based on the pairwise differences is shown to achieve the detection boundary defined by the (oracle) likelihood ratio test. We then turn to a Gaussian copula model where the marginal distributions are unknown. Standard invariance considerations lead us to consider rank tests. In fact, a higher criticism test based on the pairwise rank differences achieves the detection boundary in the normal mixture model, although not in the very sparse regime. We do not know of any rank test that has any power in that regime.

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a latent factor model for the observed data, assuming that the latent factors are independently distributed as standard normal distributions. However, the independence assumption may be unrealistic for many scenarios such as modeling multiple time series, spatial processes, and functional data, where the outcomes are correlated. In this paper, we introduce the generalized probabilistic principal component analysis (GPPCA) to study the latent factor model for multiple correlated outcomes, where each factor is modeled by a Gaussian process. Our method generalizes the previous probabilistic formulation of PCA (PPCA) by providing the closed-form maximum marginal likelihood estimator of the factor loadings and other parameters. Based on the explicit expression of the precision matrix in the marginal likelihood that we derived, the number of the computational operations is linear to the number of output variables. Furthermore, we also provide the closed-form expression of the marginal likelihood when other covariates are included in the mean structure. We highlight the advantage of GPPCA in terms of the practical relevance, estimation accuracy and computational convenience. Numerical studies of simulated and real data confirm the excellent finite-sample performance of the proposed approach.

In this paper, we extend the methodology developed for Support Vector Machines (SVM) using the $ell_2$-norm ($ell_2$-SVM) to the more general case of $ell_p$-norms with $p>1$ ($ell_p$-SVM). We derive second order cone formulations for the resulting dual and primal problems. The concept of kernel function, widely applied in $ell_2$-SVM, is extended to the more general case of $ell_p$-norms with $p>1$ by defining a new operator called multidimensional kernel. This object gives rise to reformulations of dual problems, in a transformed space of the original data, where the dependence on the original data always appear as homogeneous polynomials. We adapt known solution algorithms to efficiently solve the primal and dual resulting problems and some computational experiments on real-world datasets are presented showing rather good behavior in terms of the accuracy of $ell_p$-SVM with $p>1$.

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving noise and reward feedback. Our main theoretical result provides an explicit bound on the sample or evaluation complexity: we show that these methods are guaranteed to converge to within any pre-specified tolerance of the optimal policy with a number of zero-order evaluations that is an explicit polynomial of the error tolerance, dimension, and curvature properties of the problem. Our analysis reveals some interesting differences between the settings of additive driving noise and random initialization, as well as the settings of one-point and two-point reward feedback. Our theory is corroborated by simulations of derivative-free methods in application to these systems. Along the way, we derive convergence rates for stochastic zero-order optimization algorithms when applied to a certain class of non-convex problems.

Feature screening is a powerful tool in processing high-dimensional data. When the sample size N and the number of features p are both large, the implementation of classic screening methods can be numerically challenging. In this paper, we propose a distributed screening framework for big data setup. In the spirit of 'divide-and-conquer', the proposed framework expresses a correlation measure as a function of several component parameters, each of which can be distributively estimated using a natural U-statistic from data segments. With the component estimates aggregated, we obtain a final correlation estimate that can be readily used for screening features. This framework enables distributed storage and parallel computing and thus is computationally attractive. Due to the unbiased distributive estimation of the component parameters, the final aggregated estimate achieves a high accuracy that is insensitive to the number of data segments m. Under mild conditions, we show that the aggregated correlation estimator is as efficient as the centralized estimator in terms of the probability convergence bound and the mean squared error rate; the corresponding screening procedure enjoys sure screening property for a wide range of correlation measures. The promising performances of the new method are supported by extensive numerical examples.

Sufficient dimension reduction (SDR) is a very useful concept for exploratory analysis and data visualization in regression, especially when the number of covariates is large. Many SDR methods have been proposed for regression with a continuous response, where the central subspace (CS) is the target of estimation. Various conditions, such as the linearity condition and the constant covariance condition, are imposed so that these methods can estimate at least a portion of the CS. In this paper we study SDR for regression and discriminant analysis with categorical response. Motivated by the exploratory analysis and data visualization aspects of SDR, we propose a new geometric framework to reformulate the SDR problem in terms of manifold optimization and introduce a new concept called Maximum Separation Subspace (MASES). The MASES naturally preserves the “sufficiency” in SDR without imposing additional conditions on the predictor distribution, and directly inspires a semi-parametric estimator. Numerical studies show MASES exhibits superior performance as compared with competing SDR methods in specific settings.

Tensor Train decomposition is used across many branches of machine learning. We present T3F—a library for Tensor Train decomposition based on TensorFlow. T3F supports GPU execution, batch processing, automatic differentiation, and versatile functionality for the Riemannian optimization framework, which takes into account the underlying manifold structure to construct efficient optimization methods. The library makes it easier to implement machine learning papers that rely on the Tensor Train decomposition. T3F includes documentation, examples and 94% test coverage.

High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty quantification remains difficult --- a particular challenge is in the high complexity of estimating the cluster assignment probability under each view, and sharing information among views. In this article, we propose an approximate Bayes approach --- treating the similarity matrices generated over the views as rough first-stage estimates for the co-assignment probabilities; in its Kullback-Leibler neighborhood, we obtain a refined low-rank matrix, formed by the pairwise product of simplex coordinates. Interestingly, each simplex coordinate directly encodes the cluster assignment uncertainty. For multi-view clustering, we let each view draw a parameterization from a few candidates, leading to dimension reduction. With high model flexibility, the estimation can be efficiently carried out as a continuous optimization problem, hence enjoys gradient-based computation. The theory establishes the connection of this model to a random partition distribution under multiple views. Compared to single-view clustering approaches, substantially more interpretable results are obtained when clustering brains from a human traumatic brain injury study, using high-dimensional gene expression data.

Parametrised state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input-driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple ring (cycle) high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadratic critics and then extend it to a universal analytical method, covering a broad class of actors and critics, including Gaussian, exponential families, and policies with bounded support. For Gaussian policies, we introduce an exploration method that uses covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. For discrete action spaces, we derive a variant of EPG based on softmax policies. We also establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we provide an extensive experimental evaluation of EPG and show that it outperforms existing approaches on multiple challenging control domains.

This work is concerned with the non-negative rank-1 robust principal component analysis (RPCA), where the goal is to recover the dominant non-negative principal components of a data matrix precisely, where a number of measurements could be grossly corrupted with sparse and arbitrary large noise. Most of the known techniques for solving the RPCA rely on convex relaxation methods by lifting the problem to a higher dimension, which significantly increase the number of variables. As an alternative, the well-known Burer-Monteiro approach can be used to cast the RPCA as a non-convex and non-smooth $ell_1$ optimization problem with a significantly smaller number of variables. In this work, we show that the low-dimensional formulation of the symmetric and asymmetric positive rank-1 RPCA based on the Burer-Monteiro approach has benign landscape, i.e., 1) it does not have any spurious local solution, 2) has a unique global solution, and 3) its unique global solution coincides with the true components. An implication of this result is that simple local search algorithms are guaranteed to achieve a zero global optimality gap when directly applied to the low-dimensional formulation. Furthermore, we provide strong deterministic and probabilistic guarantees for the exact recovery of the true principal components. In particular, it is shown that a constant fraction of the measurements could be grossly corrupted and yet they would not create any spurious local solution.

Stochastic gradient Langevin dynamics (SGLD) is a fundamental algorithm in stochastic optimization. Recent work by Zhang et al. (2017) presents an analysis for the hitting time of SGLD for the first and second order stationary points. The proof in Zhang et al. (2017) is a two-stage procedure through bounding the Cheeger's constant, which is rather complicated and leads to loose bounds. In this paper, using intuitions from stochastic differential equations, we provide a direct analysis for the hitting times of SGLD to the first and second order stationary points. Our analysis is straightforward. It only relies on basic linear algebra and probability theory tools. Our direct analysis also leads to tighter bounds comparing to Zhang et al. (2017) and shows the explicit dependence of the hitting time on different factors, including dimensionality, smoothness, noise strength, and step size effects. Under suitable conditions, we show that the hitting time of SGLD to first-order stationary points can be dimension-independent. Moreover, we apply our analysis to study several important online estimation problems in machine learning, including linear regression, matrix factorization, and online PCA.

Raj Kamal Maurya, Yogesh Mani Tripathi.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 345--369.

Abstract:
We consider estimation of the multicomponent stress-strength reliability under progressive Type II censoring under the assumption that stress and strength variables follow Burr XII distributions with a common shape parameter. Maximum likelihood estimates of the reliability are obtained along with asymptotic intervals when common shape parameter may be known or unknown. Bayes estimates are also derived under the squared error loss function using different approximation methods. Further, we obtain exact Bayes and uniformly minimum variance unbiased estimates of the reliability for the case common shape parameter is known. The highest posterior density intervals are also obtained. We perform Monte Carlo simulations to compare the performance of proposed estimates and present a discussion based on this study. Finally, two real data sets are analyzed for illustration purposes.

Erlandson F. Saraiva, Adriano K. Suzuki, Luís A. Milan.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 323--344.

Abstract:
In this paper, we introduce a Bayesian approach for clustering data using a sparse finite mixture model (SFMM). The SFMM is a finite mixture model with a large number of components $k$ previously fixed where many components can be empty. In this model, the number of components $k$ can be interpreted as the maximum number of distinct mixture components. Then, we explore the use of a prior distribution for the weights of the mixture model that take into account the possibility that the number of clusters $k_{mathbf{c}}$ (e.g., nonempty components) can be random and smaller than the number of components $k$ of the finite mixture model. In order to determine clusters we develop a MCMC algorithm denominated Split-Merge allocation sampler. In this algorithm, the split-merge strategy is data-driven and was inserted within the algorithm in order to increase the mixing of the Markov chain in relation to the number of clusters. The performance of the method is verified using simulated datasets and three real datasets. The first real data set is the benchmark galaxy data, while second and third are the publicly available data set on Enzyme and Acidity, respectively.

Uttam Bandyopadhyay, Shirsendu Mukherjee, Atanu Biswas.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 291--303.

Abstract:
In adaptive crossover design, our goal is to allocate more patients to a promising treatment sequence. The present work contains a very simple three period crossover design for two competing treatments where the allocation in period 3 is done on the basis of the data obtained from the first two periods. Assuming normality of response variables we use a reliability functional for the choice between two treatments. We calculate the allocation proportions and their standard errors corresponding to the possible treatment combinations. We also derive some asymptotic results and provide solutions on related inferential problems. Moreover, the proposed procedure is compared with a possible competitor. Finally, we use a data set to illustrate the applicability of the proposed design.

Zhengwei Liu, Qi Li, Fukang Zhu.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 251--272.

Abstract:
To predict time series of counts with small values and remarkable fluctuations, an available model is the $r$ states random environment process based on the negative binomial thinning operator and the geometric marginal. However, we argue that the aforementioned model may suffer from the following two drawbacks. First, under the condition of no prior information, the overdispersed property of the geometric distribution may cause the predictions fluctuate greatly. Second, because of the constraints on the model parameters, some estimated parameters are close to zero in real-data examples, which may not objectively reveal the correlation relationship. For the first drawback, an $r$ states random environment process based on the binomial thinning operator and the Poisson marginal is introduced. For the second drawback, we propose a generalized $r$ states random environment integer-valued autoregressive model based on the binomial thinning operator to model fluctuations of data. Yule–Walker and conditional maximum likelihood estimates are considered and their performances are assessed via simulation studies. Two real-data sets are conducted to illustrate the better performances of the proposed models compared with some existing models.

David A. C. Mollinedo.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 188--201.

Abstract:
We consider the stochastic transport equation with a possibly unbounded Hölder continuous vector field. Well-posedness is proved, namely, we show existence, uniqueness and strong stability of $W^{1,p}$-weak solutions.

Mohd Arshad, Omer Abdalghani.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 167--182.

Abstract:
Suppose that $pi_{1},pi_{2},ldots ,pi_{k}$ be $k(geq2)$ independent exponential populations having unknown location parameters $mu_{1},mu_{2},ldots,mu_{k}$ and known scale parameters $sigma_{1},ldots,sigma_{k}$. Let $mu_{[k]}=max {mu_{1},ldots,mu_{k}}$. For selecting the population associated with $mu_{[k]}$, a class of selection rules (proposed by Arshad and Misra [ Statistical Papers 57 (2016) 605–621]) is considered. We consider the problem of estimating the location parameter $mu_{S}$ of the selected population under the criterion of the LINEX loss function. We consider three natural estimators $delta_{N,1},delta_{N,2}$ and $delta_{N,3}$ of $mu_{S}$, based on the maximum likelihood estimators, uniformly minimum variance unbiased estimator (UMVUE) and minimum risk equivariant estimator (MREE) of $mu_{i}$’s, respectively. The uniformly minimum risk unbiased estimator (UMRUE) and the generalized Bayes estimator of $mu_{S}$ are derived. Under the LINEX loss function, a general result for improving a location-equivariant estimator of $mu_{S}$ is derived. Using this result, estimator better than the natural estimator $delta_{N,1}$ is obtained. We also shown that the estimator $delta_{N,1}$ is dominated by the natural estimator $delta_{N,3}$. Finally, we perform a simulation study to evaluate and compare risk functions among various competing estimators of $mu_{S}$.

Abedin Haidari, Amir T. Payandeh Najafabadi, Narayanaswamy Balakrishnan.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 150--166.

Abstract:
Consider two parallel systems, say $A$ and $B$, with respective lifetimes $T_{1}$ and $T_{2}$ wherein independent component lifetimes of each system follow exponentiated generalized gamma distribution with possibly different exponential shape and scale parameters. We show here that $T_{2}$ is smaller than $T_{1}$ with respect to the usual stochastic order (reversed hazard rate order) if the vector of logarithm (the main vector) of scale parameters of System $B$ is weakly weighted majorized by that of System $A$, and if the vector of exponential shape parameters of System $A$ is unordered mojorized by that of System $B$. By means of some examples, we show that the above results can not be extended to the hazard rate and likelihood ratio orders. However, when the scale parameters of each system divide into two homogeneous groups, we verify that the usual stochastic and reversed hazard rate orders can be extended, respectively, to the hazard rate and likelihood ratio orders. The established results complete and strengthen some of the known results in the literature.

Abbas Pak, M. E. Ghitany, Mohammad Reza Mahmoudi.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 894--914.

Abstract:
This paper focuses on Bayesian estimation of the parameters and reliability function of the power Lindley distribution by using various symmetric and asymmetric loss functions. Assuming suitable priors on the parameters, Bayes estimates are derived by using squared error, linear exponential (linex) and general entropy loss functions. Since, under these loss functions, Bayes estimates of the parameters do not have closed forms we use lindley’s approximation technique to calculate the Bayes estimates. Moreover, we obtain the Bayes estimates of the parameters using a Markov Chain Monte Carlo (MCMC) method. Simulation studies are conducted in order to evaluate the performances of the proposed estimators under the considered loss functions. Finally, analysis of a real data set is presented for illustrative purposes.

Wesley Bertoli, Katiane S. Conceição, Marinho G. Andrade, Francisco Louzada.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 826--860.

Abstract:
The primary goal of this paper is to introduce the zero-modified Poisson–Lindley regression model as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros in the presence of covariates. The zero-modification is incorporated by considering that a zero-truncated process produces positive observations and consequently, the proposed model can be fitted without any previous information about the zero-modification present in a given dataset. A fully Bayesian approach based on the g-prior method has been considered for inference concerns. An intensive Monte Carlo simulation study has been conducted to evaluate the performance of the developed methodology and the maximum likelihood estimators. The proposed model was considered for the analysis of a real dataset on the number of bids received by $126$ U.S. firms between 1978–1985, and the impact of choosing different prior distributions for the regression coefficients has been studied. A sensitivity analysis to detect influential points has been performed based on the Kullback–Leibler divergence. A general comparison with some well-known regression models for discrete data has been presented.

Hedibert F. Lopes, Nicholas G. Polson.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 745--755.

Abstract:
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter values, we revisit the seminal paper of Edwards, Lindman and Savage ( Psychol. Rev. 70 (1963) 193–242). There are a number of important take-aways from comparing the Bayesian paradigm via Bayes factors to frequentist ones. We provide examples where evidence for a Bayesian strikingly supports the null, but leads to rejection under a classical test. Finally, we conclude with directions for future research.

Dani Gamerman.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 686--705.

Abstract:
Point processes are one of the most commonly encountered observation processes in Spatial Statistics. Model-based inference for them depends on the likelihood function. In the most standard setting of Poisson processes, the likelihood depends on the intensity function, and can not be computed analytically. A number of approximating techniques have been proposed to handle this difficulty. In this paper, we review recent work on exact solutions that solve this problem without resorting to approximations. The presentation concentrates more heavily on discrete time but also considers continuous time. The solutions are based on model specifications that impose smoothness constraints on the intensity function. We also review approaches to include a regression component and different ways to accommodate it while accounting for additional heterogeneity. Applications are provided to illustrate the results. Finally, we discuss possible extensions to account for discontinuities and/or jumps in the intensity function.

Davide Gabrielli, Ida Germana Minelli.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 3, 558--585.

Abstract:
Stochastic monotonicity is a well-known partial order relation between probability measures defined on the same partially ordered set. Strassen theorem establishes equivalence between stochastic monotonicity and the existence of a coupling compatible with respect to the partial order. We consider the case of a countable set and introduce the class of finitely decomposable flows on a directed acyclic graph associated to the partial order. We show that a probability measure stochastically dominates another probability measure if and only if there exists a finitely decomposable flow having divergence given by the difference of the two measures. We illustrate the result with some examples.

Daniel Ahlberg.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 397--401.

Abstract:
We study the rate of convergence in the celebrated Shape Theorem in first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are presented from a temporal perspective and complement previous work by the same author, in which the rate of convergence was studied from the standard spatial perspective.

Rodrigo Citton P. dos Reis, Enrico A. Colosimo, Gustavo L. Gilardoni.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 374--396.

Abstract:
In the data analysis from multiple repairable systems, it is usual to observe both different truncation times and heterogeneity among the systems. Among other reasons, the latter is caused by different manufacturing lines and maintenance teams of the systems. In this paper, a hierarchical model is proposed for the statistical analysis of multiple repairable systems under different truncation times. A reparameterization of the power law process is proposed in order to obtain a quasi-conjugate bayesian analysis. An empirical Bayes approach is used to estimate model hyperparameters. The uncertainty in the estimate of these quantities are corrected by using a parametric bootstrap approach. The results are illustrated in a real data set of failure times of power transformers from an electric company in Brazil.

Emilia Athayde, Assis Azevedo, Michelli Barros, Víctor Leiva.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 301--328.

Abstract:
The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.

Yong-Chao Zhang, Na Zhang.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 1, 184--191.

Abstract:
We investigate the equivalence of dynamic and static asset allocations in the case where the price process of a risky asset is driven by a Poisson process. Under some mild conditions, we obtain a necessary and sufficient condition for the equivalence of dynamic and static asset allocations. In addition, we provide a simple sufficient condition for the equivalence.

Caio L. N. Azevedo, Dalton F. Andrade

Source: Braz. J. Probab. Stat., Volume 24, Number 3, 415--433.

Abstract:
The nominal response model (NRM) was proposed by Bock [ Psychometrika 37 (1972) 29–51] in order to improve the latent trait (ability) estimation in multiple choice tests with nominal items. When the item parameters are known, expectation a posteriori or maximum a posteriori methods are commonly employed to estimate the latent traits, considering a standard symmetric normal distribution as the latent traits prior density. However, when this item set is presented to a new group of examinees, it is not only necessary to estimate their latent traits but also the population parameters of this group. This article has two main purposes: first, to develop a Monte Carlo Markov Chain algorithm to estimate both latent traits and population parameters concurrently. This algorithm comprises the Metropolis–Hastings within Gibbs sampling algorithm (MHWGS) proposed by Patz and Junker [ Journal of Educational and Behavioral Statistics 24 (1999b) 346–366]. Second, to compare, in the latent trait recovering, the performance of this method with three other methods: maximum likelihood, expectation a posteriori and maximum a posteriori. The comparisons were performed by varying the total number of items (NI), the number of categories and the values of the mean and the variance of the latent trait distribution. The results showed that MHWGS outperforms the other methods concerning the latent traits estimation as well as it recoveries properly the population parameters. Furthermore, we found that NI accounts for the highest percentage of the variability in the accuracy of latent trait estimation.