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All-Pac-12 talent Mikayla Pivec's career in Corvallis has been memorable to say the least. While it's difficult to choose just three, her top moments include a career-high 19 rebounds against Washington, a buzzer-beating layup against ASU, and breaking Ruth Hamblin's Oregon State rebounding record this year against Stanford.

Kobe Bryant was already immortal. Bryant and fellow NBA greats Tim Duncan and Kevin Garnett headlined a nine-person group announced Saturday as this year’s class of enshrinees into the Naismith Memorial Basketball Hall of Fame. Two-time NBA champion coach Rudy Tomjanovich finally got his call, as did longtime Baylor women’s coach Kim Mulkey, 1,000-game winner Barbara Stevens of Bentley and three-time Final Four coach Eddie Sutton.

For Vic Schaefer, the decision to take over the Texas women's basketball program was profoundly personal. “It was a calling,” Schaefer said Monday, noting the old Austin hospital building where he was born is just across the street from where the Longhorns play at the Frank Erwin Center. Texas quickly snatched up Schaefer on Sunday, just two days after athletic director Chris Del Conte announced coach Karen Aston would not be retained after eight seasons.

COLUMBIA, S.C. (AP) -- South Carolina freshman Aliyah Boston has won the Lisa Leslie Award given to the top center in women’s college basketball.

South Carolina coach Dawn Staley believes her top-ranked Gamecocks are the women's basketball national champions, even without an NCAA Tournament trophy to put in their display case due to the pandemic-shortened season. The NCAA decided against officially crowning champions after its signature tournaments were called off due to the coronavirus pandemic that has sent much of the world into lock down. Staley spoke from her home where she's spent the past month managing her program and ensuring her players don't linger too much on what they missed.

Ruthy Hebard, who ranks 2nd in Oregon history in points (2,368) and 3rd in rebounds (1,299), prepares to play in the WNBA following four years in Eugene. Hebard is the Oregon and Pac-12 all-time leader in career field-goal percentage (65.1) and averaged 17.3 points per game and a career-high 9.6 rebounds per game as a senior.

The Tennessee Lady Vols have added forward-center Keyen Green as a graduate transfer from Liberty. Coach Kellie Harper announced Wednesday that Green has signed a scholarship for the upcoming season. The 6-foot-1 Green spent the past four seasons at Liberty and graduated in May 2019.

Pac-12 Networks' Ashley Adamson speaks with former Arizona State women's basketball player Michelle Tom, who is now a doctor treating COVID-19 patients in Winslow, Arizona.

During Wednesday's "Pac-12 Perspective" podcast, Natalie Chou shared why she is using her platform to speak out against racism she sees in her community related to the novel coronavirus.

Pac-12 Networks' Mike Yam has a conversation with UCLA's Natalie Chou during Wednesday's "Pac-12 Perspective" podcast. Chou reflects on her role models, passion for basketball and how her mom has made a big impact on her hoops career.

Watch the debut of "Our Stories - Natalie Chou" on Sunday, May 10 at 12:30 p.m. PT/ 1:30 p.m. MT on Pac-12 Network.

Eunji Lim.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 2053--2097.

Abstract:
We study the asymptotic behavior of the least squares estimators when the model is possibly misspecified. We consider the setting where we wish to estimate an unknown function $f_{*}:(0,1)^{d} ightarrow mathbb{R}$ from observations $(X,Y),(X_{1},Y_{1}),cdots ,(X_{n},Y_{n})$; our estimator $hat{g}_{n}$ is the minimizer of $sum _{i=1}^{n}(Y_{i}-g(X_{i}))^{2}/n$ over $gin mathcal{G}$ for some set of functions $mathcal{G}$. We provide sufficient conditions on the metric entropy of $mathcal{G}$, under which $hat{g}_{n}$ converges to $g_{*}$ as $n ightarrow infty $, where $g_{*}$ is the minimizer of $|g-f_{*}| riangleq mathbb{E}(g(X)-f_{*}(X))^{2}$ over $gin mathcal{G}$. As corollaries of our theorem, we establish $|hat{g}_{n}-g_{*}| ightarrow 0$ as $n ightarrow infty $ when $mathcal{G}$ is the set of monotone functions or the set of convex functions. We also make a connection between the convergence rate of $|hat{g}_{n}-g_{*}|$ and the metric entropy of $mathcal{G}$. As special cases of our finding, we compute the convergence rate of $|hat{g}_{n}-g_{*}|^{2}$ when $mathcal{G}$ is the set of bounded monotone functions or the set of bounded convex functions.

Maddalena Cavicchioli.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 605--631.

Abstract:
The paper treats the modeling of stationary multivariate stochastic processes via a frequency domain model expressed in terms of cepstrum theory. The proposed model nests the vector exponential model of [20] as a special case, and extends the generalised cepstral model of [36] to the multivariate setting, answering a question raised by the last authors in their paper. Contemporarily, we extend the notion of generalised autocovariance function of [35] to vector time series. Then we derive explicit matrix formulas connecting generalised cepstral and autocovariance matrices of the process, and prove the consistency and asymptotic properties of the Whittle likelihood estimators of model parameters. Asymptotic theory for the special case of the vector exponential model is a significant addition to the paper of [20]. We also provide a mathematical machinery, based on matrix differentiation, and computational methods to derive our results, which differ significantly from those employed in the univariate case. The utility of the proposed model is illustrated through Monte Carlo simulation from a bivariate process characterized by a high dynamic range, and an empirical application on time varying minimum variance hedge ratios through the second moments of future and spot prices in the corn commodity market.

Olivier Roustant, Fabrice Gamboa, Bertrand Iooss.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 386--412.

Abstract:
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol’ sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol’ indices with Parseval equalities and give general lower bounds for these indices obtained by truncation. The case of the eigenfunctions system associated with a Poincaré differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.

François Bachoc, José Betancourt, Reinhard Furrer, Thierry Klein.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1962--2008.

Abstract:
The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of non-Gaussian processes obtained by regular non-linear transformations of Gaussian processes. We provide the increasing-domain asymptotic properties of the (Gaussian) maximum likelihood and cross validation estimators of the covariance parameters of a non-Gaussian process of this class. We show that these estimators are consistent and asymptotically normal, although they are defined as if the process was Gaussian. They do not need to model or estimate the non-linear transformation. Our results can thus be interpreted as a robustness of (Gaussian) maximum likelihood and cross validation towards non-Gaussianity. Our proofs rely on two technical results that are of independent interest for the increasing-domain asymptotic literature of spatial processes. First, we show that, under mild assumptions, coefficients of inverses of large covariance matrices decay at an inverse polynomial rate as a function of the corresponding observation location distances. Second, we provide a general central limit theorem for quadratic forms obtained from transformed Gaussian processes. Finally, our asymptotic results are illustrated by numerical simulations.

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.

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.

David Azriel, Armin Schwartzman.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 174--206.

Abstract:
In this work we study estimation of signals when the number of parameters is much larger than the number of observations. A large body of literature assumes for these kind of problems a sparse structure where most of the parameters are zero or close to zero. When this assumption does not hold, one can focus on low-dimensional functions of the parameter vector. In this work we study one-dimensional linear projections. Specifically, in the context of high-dimensional linear regression, the parameter of interest is ${oldsymbol{eta}}$ and we study estimation of $mathbf{a}^{T}{oldsymbol{eta}}$. We show that $mathbf{a}^{T}hat{oldsymbol{eta}}$, where $hat{oldsymbol{eta}}$ is the least squares estimator, using pseudo-inverse when $p>n$, is minimax and admissible. Thus, for linear projections no regularization or shrinkage is needed. This estimator is easy to analyze and confidence intervals can be constructed. We study a high-dimensional dataset from brain imaging where it is shown that the signal is weak, non-sparse and significantly different from zero.

Matthias Löwe, Kristina Schubert.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1796--1815.

Abstract:
We show how to exactly reconstruct the block structure at the critical line in the so-called Ising block model. This model was recently re-introduced by Berthet, Rigollet and Srivastava in [2]. There the authors show how to exactly reconstruct blocks away from the critical line and they give an upper and a lower bound on the number of observations one needs; thereby they establish a minimax optimal rate (up to constants). Our technique relies on a combination of their methods with fluctuation results obtained in [20]. The latter are extended to the full critical regime. We find that the number of necessary observations depends on whether the interaction parameter between two blocks is positive or negative: In the first case, there are about $Nlog N$ observations required to exactly recover the block structure, while in the latter case $sqrt{N}log N$ observations suffice.

Gwenaëlle Castellan, Anthony Cousien, Viet Chi Tran.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 50--81.

Abstract:
Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output’s variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators.

Guanyang Wang.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1690--1706.

Abstract:
Uniform sampling of binary matrix with fixed margins is an important and difficult problem in statistics, computer science, ecology and so on. The well-known swap algorithm would be inefficient when the size of the matrix becomes large or when the matrix is too sparse/dense. Here we propose the Rectangle Loop algorithm, a Markov chain Monte Carlo algorithm to sample binary matrices with fixed margins uniformly. Theoretically the Rectangle Loop algorithm is better than the swap algorithm in Peskun’s order. Empirically studies also demonstrates the Rectangle Loop algorithm is remarkablely more efficient than the swap algorithm.

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.

Xuening Zhu.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1413--1448.

Abstract:
High dimensional time series receive considerable attention recently, whose temporal and cross-sectional dependency could be captured by the vector autoregression (VAR) model. To tackle with the high dimensionality, penalization methods are widely employed. However, theoretically, the existing studies of the penalization methods mainly focus on $i.i.d$ data, therefore cannot quantify the effect of the dependence level on the convergence rate. In this work, we use the spectral properties of the time series to quantify the dependence and derive a nonasymptotic upper bound for the estimation errors. By focusing on the nonconcave penalization methods, we manage to establish the oracle properties of the penalized VAR model estimation by considering the effects of temporal and cross-sectional dependence. Extensive numerical studies are conducted to compare the finite sample performance using different penalization functions. Lastly, an air pollution data of mainland China is analyzed for illustration purpose.

Ryoya Oda, Hirokazu Yanagihara.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1386--1412.

Abstract:
We put forward a variable selection method for selecting explanatory variables in a normality-assumed multivariate linear regression. It is cumbersome to calculate variable selection criteria for all subsets of explanatory variables when the number of explanatory variables is large. Therefore, we propose a fast and consistent variable selection method based on a generalized $C_{p}$ criterion. The consistency of the method is provided by a high-dimensional asymptotic framework such that the sample size and the sum of the dimensions of response vectors and explanatory vectors divided by the sample size tend to infinity and some positive constant which are less than one, respectively. Through numerical simulations, it is shown that the proposed method has a high probability of selecting the true subset of explanatory variables and is fast under a moderate sample size even when the number of dimensions is large.

Zhixin Zhou, Ping Li.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1302--1347.

Abstract:
The Chernoff coefficient is known to be an upper bound of Bayes error probability in classification problem. In this paper, we will develop a rate optimal Chernoff bound on the Bayes error probability. The new bound is not only an upper bound but also a lower bound of Bayes error probability up to a constant factor. Moreover, we will apply this result to community detection in the stochastic block models. As a clustering problem, the optimal misclassification rate of community detection problem can be characterized by our rate optimal Chernoff bound. This can be formalized by deriving a minimax error rate over certain parameter space of stochastic block models, then achieving such an error rate by a feasible algorithm employing multiple steps of EM type updates.

Vincent Brault, Christine Keribin, Mahendra Mariadassou.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1234--1268.

Abstract:
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have been proposed and are now well understood empirically, theoretical guarantees about their asymptotic behavior is rather sparse and most results are limited to the binary setting. We prove here theoretical guarantees in the valued settings. We show that under some mild conditions on the parameter space, and in an asymptotic regime where $log (d)/n$ and $log (n)/d$ tend to $0$ when $n$ and $d$ tend to infinity, (1) the maximum-likelihood estimate of the complete model (with known labels) is consistent and (2) the log-likelihood ratios are equivalent under the complete and observed (with unknown labels) models. This equivalence allows us to transfer the asymptotic consistency, and under mild conditions, asymptotic normality, to the maximum likelihood estimate under the observed model. Moreover, the variational estimator is also consistent and, under the same conditions, asymptotically normal.

Mario Teixeira Parente, Jonas Wallin, Barbara Wohlmuth.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 917--943.

Abstract:
In this article, we consider scenarios in which traditional estimates for the active subspace method based on probabilistic Poincaré inequalities are not valid due to unbounded Poincaré constants. Consequently, we propose a framework that allows to derive generalized estimates in the sense that it enables to control the trade-off between the size of the Poincaré constant and a weaker order of the final error bound. In particular, we investigate independently exponentially distributed random variables in dimension two or larger and give explicit expressions for corresponding Poincaré constants showing their dependence on the dimension of the problem. Finally, we suggest possibilities for future work that aim for extending the class of distributions applicable to the active subspace method as we regard this as an opportunity to enlarge its usability.

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.

Alessandro Casa, José E. Chacón, Giovanna Menardi.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 835--856.

Abstract:
Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows framing the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.