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Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in…

Probability · Mathematics 2015-09-08 Yannick Baraud

A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.

Probability · Mathematics 2025-03-27 Alina Akhmiarova , Alexander Veretennikov

A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…

Probability · Mathematics 2018-06-12 Alexander V. Ivanov , Igor V. Orlovskyi

The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…

Methodology · Statistics 2016-09-06 Yi-Hui Zhou

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Methodology · Statistics 2017-12-12 Yi-Hui Zhou

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…

Probability · Mathematics 2024-11-14 Manjunath Krishnapur , D. Yogeshwaran

This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper…

Statistics Theory · Mathematics 2021-07-20 Martin Wahl

The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent…

Statistics Theory · Mathematics 2019-05-27 Fang Han , Yicheng Li

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…

Machine Learning · Statistics 2017-10-20 Addison Hu , Sahand Negahban

We present a weighted estimator of the covariance and correlation in bipartite complex systems with a double layer of heterogeneity. The advantage provided by the weighted estimators lies in the fact that the unweighted sample covariance…

Data Analysis, Statistics and Probability · Physics 2016-12-22 Elena Puccio , Jyrki Piilo , Michele Tumminello

In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…

Methodology · Statistics 2019-02-12 Siliang Gong , Kai Zhang , Yufeng Liu

This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…

Numerical Analysis · Mathematics 2018-11-13 Arvind K. Saibaba

This paper derives sufficient conditions for superconvergence of sums of bounded free random variables and provides an estimate for the rate of superconvergence.

Probability · Mathematics 2007-10-23 Vladislav Kargin

This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…

Statistics Theory · Mathematics 2021-01-25 Weiming Li , Qinwen Wang , Jianfeng Yao , Wang Zhou

In this paper, we study a bi-criterion framework for assessing scoring functions in the context of binary classification. The positive and negative predictive values (ppv and npv, respectively) are conditional probabilities of the true…

Machine Learning · Statistics 2020-07-13 Keshav Vemuri , Nathan Srebro

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance…

Machine Learning · Computer Science 2023-06-06 Kyurae Kim , Kaiwen Wu , Jisu Oh , Jacob R. Gardner

Some of the tightest information-theoretic generalization bounds depend on the average information between the learned hypothesis and a single training example. However, these sample-wise bounds were derived only for expected generalization…

Machine Learning · Computer Science 2022-12-14 Hrayr Harutyunyan , Greg Ver Steeg , Aram Galstyan

We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…

Probability · Mathematics 2017-03-08 Bero Roos

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

Methodology · Statistics 2017-03-22 Hachem Saddiki , Andrew C. Trapp , Patrick Flaherty