A union lobbyist who worked just one day as a substitute teacher is entitled to a pension worth potentially tens of thousands of dollars annually, the Illinois supreme court has ruled.

The San Jose Sharks are considering different scenarios in how to handle the return of hockey. The questions the Sharks are asking themselves are likely the same ones the Caps are as everyone waits for the end of the coronavirus pandemic.

Ducks defensemen Christian Djoos and Jani Hakanpaa will stay with the team through the 2020-21 season after each signed a one-year, one-way contract extension.

The Bruins, Predators, Avalanche, and Blue Jackets were set to play games in Mannheim, Bern, Prague, and Helsinki.

The Boston Bruins had planned on opening up their 2020-21 NHL regular season overseas against the Nashville Predators in Prague as part of the NHL Global Series, but that plan to visit the Czech Republic has now been postponed.

The NHL announces it is postponing the Global Series games that were scheduled to be held in the Czech Republic and Finland in the 2020-21 season.

Gov. Erik Greitens has resigned and the board doesn't have enough governor-appointed members to form a quorum. Important tasks have been piling up.

Former Missouri education Commissioner Margie Vandeven, who was fired by by the state's board of education, has been rehired.

Berkeley, California : Tabor Sarah Books, 1988.

Rockville, Maryland : The National Institute on Drug Abuse, 1976.

Rockville, Maryland : U.S. Dept. of Health, Education, and Welfare, Public Health Service, Alcohol, Drug Abuse and Mental Health Administration, 1976.

Rockville, Maryland : National Institute on Drug Abuse, 1985.

Rockville, Maryland : National Institute on Drug Abuse, 1980.

London : European Collaborating Centres in Addiction Studies, 1998.

Sabrina Ionescu is the Naismith Trophy Player of the Year, concluding her illustrious Oregon career with one of the major postseason women's basketball awards. As the only player in college basketball history with 2,000 career points (2,562), 1,000 assists (1,091) and 1,000 rebounds (1,040) and the NCAA all-time leader with 26 triple-doubles, Ionescu has continued to rack up player of the year honors for her remarkable senior season.

Already named The Associated Press women's player of the year, Ionescu was awarded the Naismith Trophy for the most outstanding women's basketball player on Friday. Ionescu, who won AP All-American honors three times, shattered the NCAA career triple-double mark with 26 and became the first player in college history to have 2,000 points, 1,000 rebounds and 1,000 assists. Ionescu averaged 17.5 points, 9.1 assists and 8.6 rebounds with eight triple-doubles as a senior this season.

Sabrina Ionescu wins the Wooden Award for the second year in a row, becoming the fifth in the trophy's history to win in back-to-back seasons. With the honor, she completes a complete sweep of the national postseason player of the year awards. As a senior, Ionescu matched her own single-season mark with eight triple-doubles in 2019-20, and she was incredibly efficient from the field with a career-best 51.8 field goal percentage.

Pac-12 Networks' Ashley Adamson speaks with Oregon stars Sabrina Ionescu, Ruthy Hebard and Satou Sabally to hear how special their recent Naismith Starting 5 honor was, as the Ducks comprise three of the nation's top five players. Ionescu (point guard), Sabally (small forward) and Hebard (power forward) led the Ducks to a 31-2 record in the 2019-20 season before it was cut short.

Pac-12 Networks' Ashley Adamson catches up with Oregon's "Big 3" of Sabrina Ionescu, Ruthy Hebard and Satou Sabally to hear how they're adjusting to the new world without sports while still preparing for the WNBA Draft on April 17. They also share how they're staying hungry for basketball during the hiatus.

After sweeping every national player of the year award, Sabrina Ionescu is off to the WNBA level where her skills will make an instant impact — not just to her new team but the league as a whole. She averaged 17.5 points, 8.6 rebounds and 9.1 assists for the Ducks in 2019-20, rewriting her own NCAA career triple-double record and becoming the first in college basketball history with at least 2,000 points, 1,000 rebounds and 1,000 assists.

Watch "Our Stories Unfinished Business: Sabrina Ionescu and Ruthy Hebard" debuting Wednesday, April 15 at 7 p.m. PT/ 8 p.m. MT on Pac-12 Network.

Learn how Oregon stars Sabrina Ionescu and Ruthy Hebard developed a lasting bond as college freshmen and carried that through storied four-year careers for the Ducks. Watch "Our Stories Unfinished Business: Sabrina Ionescu and Ruthy Hebard" debuting Wednesday, April 15 at 7 p.m. PT/ 8 p.m. MT on Pac-12 Network.

Ruthy Hebard and Sabrina Ionescu have had a remarkable four years together in Eugene, rewriting the history books and pushing the Ducks into the national spotlight. Catch the debut of "Our Stories Unfinished Business: Sabrina Ionescu and Ruthy Hebard" at Wednesday, April 15 at 7 p.m. PT/ 8 p.m. MT on Pac-12 Network.

With the spotlight on her growing ever brighter, Sabrina Ionescu is aware she's becoming her own brand. One of the most decorated players in women's college basketball, Ionescu is about to go pro with the WNBA draft coming up Friday. Ionescu said Oregon has prepared her to understand how much impact she can have in the community and on women's basketball.

Notre Dame coach Muffet McGraw retired after 33 seasons Wednesday. What she did for me in those four years, I came in as a girl and left as a woman.'' - WNBA player Kayla McBride, who played for Notre Dame from 2010-14.

See some of Sabrina Ionescu's remarkable accomplishments at Oregon set to the Star Wars opening crawl.

During Friday's "Pac-12 Perspective," Stanford head coach Tara VanDerveer spoke about Haley Jones' positionless game and how the Cardinal used the dynamic freshman in 2019-20. Download and listen wherever you get your podcasts.

Alexandre Mösching, Lutz Dümbgen.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 24--49.

Abstract:
We consider bivariate observations $(X_{1},Y_{1}),ldots,(X_{n},Y_{n})$ such that, conditional on the $X_{i}$, the $Y_{i}$ are independent random variables. Precisely, the conditional distribution function of $Y_{i}$ equals $F_{X_{i}}$, where $(F_{x})_{x}$ is an unknown family of distribution functions. Under the sole assumption that $xmapsto F_{x}$ is isotonic with respect to stochastic order, one can estimate $(F_{x})_{x}$ in two ways: (i) For any fixed $y$ one estimates the antitonic function $xmapsto F_{x}(y)$ via nonparametric monotone least squares, replacing the responses $Y_{i}$ with the indicators $1_{[Y_{i}le y]}$. (ii) For any fixed $eta in (0,1)$ one estimates the isotonic quantile function $xmapsto F_{x}^{-1}(eta)$ via a nonparametric version of regression quantiles. We show that these two approaches are closely related, with (i) being more flexible than (ii). Then, under mild regularity conditions, we establish rates of convergence for the resulting estimators $hat{F}_{x}(y)$ and $hat{F}_{x}^{-1}(eta)$, uniformly over $(x,y)$ and $(x,eta)$ in certain rectangles as well as uniformly in $y$ or $eta$ for a fixed $x$.

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.

Kentaro Minami.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1508--1576.

Abstract:
We study the problem of estimating piecewise monotone vectors. This problem can be seen as a generalization of the isotonic regression that allows a small number of order-violating changepoints. We focus mainly on the performance of the nearly-isotonic regression proposed by Tibshirani et al. (2011). We derive risk bounds for the nearly-isotonic regression estimators that are adaptive to piecewise monotone signals. The estimator achieves a near minimax convergence rate over certain classes of piecewise monotone signals under a weak assumption. Furthermore, we present an algorithm that can be applied to the nearly-isotonic type estimators on general weighted graphs. The simulation results suggest that the nearly-isotonic regression performs as well as the ideal estimator that knows the true positions of changepoints.

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.

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for the local inferences; these weakened priors may not provide enough regularization for each separate computation, thus eliminating one of the key advantages of Bayesian methods. To resolve this dilemma while still retaining the generalizability of the underlying local inference method, we apply the idea of expectation propagation (EP) as a framework for distributed Bayesian inference. The central idea is to iteratively update approximations to the local likelihoods given the state of the other approximations and the prior. The present paper has two roles: we review the steps that are needed to keep EP algorithms numerically stable, and we suggest a general approach, inspired by EP, for approaching data partitioning problems in a way that achieves the computational benefits of parallelism while allowing each local update to make use of relevant information from the other sites. In addition, we demonstrate how the method can be applied in a hierarchical context to make use of partitioning of both data and parameters. The paper describes a general algorithmic framework, rather than a specific algorithm, and presents an example implementation for it.

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.

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.

In many areas, practitioners need to analyze large data sets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high-dimensional random-effects model where each predictor has a small effect, we discover several new phenomena. Infinite-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call 'infinite-worker limit'. Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are suboptimal. We also propose a new Weighted ONe-shot DistributEd Ridge regression algorithm (WONDER). We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy.

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.

Danilo Covaes Nogarotto, Caio Lucidius Naberezny Azevedo, Jorge Luis Bazán.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 304--322.

Abstract:
The interest on the analysis of the zero–one augmented beta regression (ZOABR) model has been increasing over the last few years. In this work, we developed a Bayesian inference for the ZOABR model, providing some contributions, namely: we explored the use of Jeffreys-rule and independence Jeffreys prior for some of the parameters, performing a sensitivity study of prior choice, comparing the Bayesian estimates with the maximum likelihood ones and measuring the accuracy of the estimates under several scenarios of interest. The results indicate, in a general way, that: the Bayesian approach, under the Jeffreys-rule prior, was as accurate as the ML one. Also, different from other approaches, we use the predictive distribution of the response to implement Bayesian residuals. To further illustrate the advantages of our approach, we conduct an analysis of a real psychometric data set including a Bayesian residual analysis, where it is shown that misleading inference can be obtained when the data is transformed. That is, when the zeros and ones are transformed to suitable values and the usual beta regression model is considered, instead of the ZOABR model. Finally, future developments are discussed.

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.

Natalia Shenkman.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 127--135.

Abstract:
While derivations of the characterization of the $d$-variate exchangeable Marshall–Olkin copula via $d$-monotone sequences relying on basic knowledge in probability theory exist in the literature, they contain a myriad of unnecessary relatively complicated computations. We revisit this issue and provide proofs where all undesired artefacts are removed, thereby exposing the simplicity of the characterization. In particular, we give an insightful analytical derivation of the monotonicity conditions based on the monotonicity properties of the survival probabilities.

Solveig Engebretsen, Ingrid K. Glad.

Source: Statistics Surveys, Volume 13, 1--51.

Abstract:
In numerous problems where the aim is to estimate the effect of a predictor variable on a response, one can assume a monotone relationship. For example, dose-effect models in medicine are of this type. In a multiple regression setting, additive monotone regression models assume that each predictor has a monotone effect on the response. In this paper, we present an overview and comparison of very recent frequentist methods for fitting additive monotone regression models. Three of the methods we present can be used both in the high dimensional setting, where the number of parameters $p$ exceeds the number of observations $n$, and in the classical multiple setting where $1<pleq n$. However, many of the most recent methods only apply to the classical setting. The methods are compared through simulation experiments in terms of efficiency, prediction error and variable selection properties in both settings, and they are applied to the Boston housing data. We conclude with some recommendations on when the various methods perform best.

Mariella Dimiccoli.

Source: Statistics Surveys, Volume 10, 53--99.

Abstract:
Cone regression is a particular case of quadratic programming that minimizes a weighted sum of squared residuals under a set of linear inequality constraints. Several important statistical problems such as isotonic, concave regression or ANOVA under partial orderings, just to name a few, can be considered as particular instances of the cone regression problem. Given its relevance in Statistics, this paper aims to address the fundamentals of cone regression from a theoretical and practical point of view. Several formulations of the cone regression problem are considered and, focusing on the particular case of concave regression as an example, several algorithms are analyzed and compared both qualitatively and quantitatively through numerical simulations. Several improvements to enhance numerical stability and bound the computational cost are proposed. For each analyzed algorithm, the pseudo-code and its corresponding code in Matlab are provided. The results from this study demonstrate that the choice of the optimization approach strongly impacts the numerical performances. It is also shown that methods are not currently available to solve efficiently cone regression problems with large dimension (more than many thousands of points). We suggest further research to fill this gap by exploiting and adapting classical multi-scale strategy to compute an approximate solution.