São Paulo : Serviço Grafíco da Secretaria da Segurança Pública, 1976.

São Paulo : Serviço Grafíco da Secretaria da Segurança Pública, 1976.

[West Point, Pa.] : [Merck Sharp & Dohme], [1977?]

Helsinki : Department of Pharmacology and Toxicology, University of Helsinki, 1985.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

London : Reproductive Health Matters, 1993-2018.

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.

LEXINGTON, Ky. (AP) -- Sophomore guards Jazmine Massengill and Robyn Benton transferred to Kentucky from Southeastern Conference rivals Wednesday.

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.

Pac-12 Networks' Yogi Roth and Ashley Adamson talk with Hall of Fame player and Pac-12 Networks talent Bill Walton during Thursday's Pac-12 Perspective podcast.

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.

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.

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.

Emanuel Ben-David, Bala Rajaratnam.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 580--604.

Abstract:
The Wishart distribution defined on the open cone of positive-definite matrices plays a central role in multivariate analysis and multivariate distribution theory. Its domain of parameters is often referred to as the Gindikin set. In recent years, varieties of useful extensions of the Wishart distribution have been proposed in the literature for the purposes of studying Markov random fields and graphical models. In particular, generalizations of the Wishart distribution, referred to as Type I and Type II (graphical) Wishart distributions introduced by Letac and Massam in Annals of Statistics (2007) play important roles in both frequentist and Bayesian inference for Gaussian graphical models. These distributions have been especially useful in high-dimensional settings due to the flexibility offered by their multiple-shape parameters. Concerning Type I and Type II Wishart distributions, a conjecture of Letac and Massam concerns the domain of multiple-shape parameters of these distributions. The conjecture also has implications for the existence of Bayes estimators corresponding to these high dimensional priors. The conjecture, which was first posed in the Annals of Statistics, has now been an open problem for about 10 years. In this paper, we give a necessary condition for the Letac and Massam conjecture to hold. More precisely, we prove that if the Letac and Massam conjecture holds on a decomposable graph, then no two separators of the graph can be nested within each other. For this, we analyze Type I and Type II Wishart distributions on appropriate Markov equivalent perfect DAG models and succeed in deriving the aforementioned necessary condition. This condition in particular identifies a class of counterexamples to the conjecture.

Gregor Pasemann, Wilhelm Stannat.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 547--579.

Abstract:
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part. Emphasis is put on the case of stochastic reaction-diffusion systems. Robustness results for statistical inference under model uncertainty are provided.

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.

Ming Yu, Varun Gupta, Mladen Kolar.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 413--457.

Abstract:
We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We propose a GDT (Gradient Descent with hard Thresholding) algorithm to efficiently recover matrices with such structure, by minimizing a bi-convex function over a nonconvex set of constraints. We show linear convergence of the iterates obtained by GDT to a region within statistical error of an optimal solution. As an application of our method, we consider multi-task learning problems and show that the statistical error rate obtained by GDT is near optimal compared to minimax rate. Experiments demonstrate competitive performance and much faster running speed compared to existing methods, on both simulations and real data sets.

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.

Arvind Prasadan, Raj Rao Nadakuditi, Debashis Paul.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 345--385.

Abstract:
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the number of samples. Below this critical eigen-SNR, the estimates returned by the SVD are asymptotically uncorrelated with the latent principal components. We consider a setting where the left singular vector of the underlying rank one signal matrix is assumed to be sparse and the right singular vector is assumed to be equisigned, that is, having either only nonnegative or only nonpositive entries. We consider six different algorithms for estimating the sparse principal component based on different statistical criteria and prove that by exploiting sparsity, we recover consistent estimates in the low eigen-SNR regime where the SVD fails. Our analysis reveals conditions under which a coordinate selection scheme based on a sum-type decision statistic outperforms schemes that utilize the $ell _{1}$ and $ell _{2}$ norm-based statistics. We derive lower bounds on the size of detectable coordinates of the principal left singular vector and utilize these lower bounds to derive lower bounds on the worst-case risk. Finally, we verify our findings with numerical simulations and a illustrate the performance with a video data where the interest is in identifying objects.

Wanli Qiao.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 302--344.

Abstract:
Bandwidth selection is crucial in the kernel estimation of density level sets. A risk based on the symmetric difference between the estimated and true level sets is usually used to measure their proximity. In this paper we provide an asymptotic $L^{p}$ approximation to this risk, where $p$ is characterized by the weight function in the risk. In particular the excess risk corresponds to an $L^{2}$ type of risk, and is adopted to derive an optimal bandwidth for nonparametric level set estimation of $d$-dimensional density functions ($dgeq 1$). A direct plug-in bandwidth selector is developed for kernel density level set estimation and its efficacy is verified in numerical studies.

Gianluca Finocchio, Johannes Schmidt-Hieber.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 239--271.

Abstract:
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE) for $sigma^{2}$ is biased and inconsistent. This raises the question whether the posterior is able to correct the MLE in this case. By developing a new proving strategy that uses refined properties of the posterior distribution, we find that the marginal posterior is inconsistent for any i.i.d. prior on the mean parameters. In particular, no assumption on the decay of the prior needs to be imposed. Surprisingly, we also find that consistency can be retained for a hierarchical prior based on Gaussian mixtures. In this case we also establish a limiting shape result and determine the limit distribution. In contrast to the classical Bernstein-von Mises theorem, the limit is non-Gaussian. We show that the Bayesian analysis leads to new statistical estimators outperforming the correctly calibrated MLE in a numerical simulation study.

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.

Heiko Werner, Hajo Holzmann, Pierre Vandekerkhove.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1816--1871.

Abstract:
We investigate a flexible two-component semiparametric mixture of regressions model, in which one of the conditional component distributions of the response given the covariate is unknown but assumed symmetric about a location parameter, while the other is specified up to a scale parameter. The location and scale parameters together with the proportion are allowed to depend nonparametrically on covariates. After settling identifiability, we provide local M-estimators for these parameters which converge in the sup-norm at the optimal rates over Hölder-smoothness classes. We also introduce an adaptive version of the estimators based on the Lepski-method. Sup-norm bounds show that the local M-estimator properly estimates the functions globally, and are the first step in the construction of useful inferential tools such as confidence bands. In our analysis we develop general results about rates of convergence in the sup-norm as well as adaptive estimation of local M-estimators which might be of some independent interest, and which can also be applied in various other settings. We investigate the finite-sample behaviour of our method in a simulation study, and give an illustration to a real data set from bioinformatics.

Tuo Chen, Zhihua Su, Yi Yang, Shanshan Ding.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 143--173.

Abstract:
As a generalization of the classical linear regression, expectile regression (ER) explores the relationship between the conditional expectile of a response variable and a set of predictor variables. ER with respect to different expectile levels can provide a comprehensive picture of the conditional distribution of the response variable given the predictors. We adopt an efficient estimation method called the envelope model ([8]) in ER, and construct a novel envelope expectile regression (EER) model. Estimation of the EER parameters can be performed using the generalized method of moments (GMM). We establish the consistency and derive the asymptotic distribution of the EER estimators. In addition, we show that the EER estimators are asymptotically more efficient than the ER estimators. Numerical experiments and real data examples are provided to demonstrate the efficiency gains attained by EER compared to ER, and the efficiency gains can further lead to improvements in prediction.

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.

Daniel R. Kowal, Antonio Canale.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1744--1772.

Abstract:
We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeling zero-inflation, bounded or censored data, and over- or underdispersion. The transformation is modeled as unknown for greater distributional flexibility, while the rounding operation ensures a coherent integer-valued data-generating process. An efficient MCMC algorithm is developed for posterior inference and provides a mechanism for adaptation of successful Bayesian models and algorithms for continuous data to the integer-valued data setting. Using the STAR framework, we design a new Bayesian Additive Regression Tree model for integer-valued data, which demonstrates impressive predictive distribution accuracy for both synthetic data and a large healthcare utilization dataset. For interpretable regression-based inference, we develop a STAR additive model, which offers greater flexibility and scalability than existing integer-valued models. The STAR additive model is applied to study the recent decline in Amazon river dolphins.

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.

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.

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.

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.

Rahul Mazumder, Haolei Weng.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1348--1385.

Abstract:
Estimating a low rank matrix from its linear measurements is a problem of central importance in contemporary statistical analysis. The choice of tuning parameters for estimators remains an important challenge from a theoretical and practical perspective. To this end, Stein’s Unbiased Risk Estimate (SURE) framework provides a well-grounded statistical framework for degrees of freedom estimation. In this paper, we use the SURE framework to obtain degrees of freedom estimates for a general class of spectral regularized matrix estimators—our results generalize beyond the class of estimators that have been studied thus far. To this end, we use a result due to Shapiro (2002) pertaining to the differentiability of symmetric matrix valued functions, developed in the context of semidefinite optimization algorithms. We rigorously verify the applicability of Stein’s Lemma towards the derivation of degrees of freedom estimates; and also present new techniques based on Gaussian convolution to estimate the degrees of freedom of a class of spectral estimators, for which Stein’s Lemma does not directly apply.

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.