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We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…

Statistics Theory · Mathematics 2022-07-04 Nikolas Siapoutis , Donald Richards , Bharath K. Sriperumbudur

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Statistics Theory · Mathematics 2008-02-20 Joseph Rynkiewicz

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample…

Applications · Statistics 2018-02-14 Augusto Aubry , Antonio De Maio , Luca Pallotta

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet…

Statistics Theory · Mathematics 2010-10-20 T. Tony Cai , Cun-Hui Zhang , Harrison H. Zhou

The problem of estimating a spiked covariance matrix in high dimensions under Frobenius loss, and the parallel problem of estimating the noise in spiked PCA is investigated. We propose an estimator of the noise parameter by minimizing an…

Statistics Theory · Mathematics 2014-08-28 Didier Chételat , Martin T. Wells

Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function.…

Statistics Theory · Mathematics 2011-01-19 Reman Abu-Shanab , John T. Kent , William E. Strawderman

Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…

Methodology · Statistics 2016-05-30 Qiong Li , Xin Gao , Helene Massam

We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…

Statistics Theory · Mathematics 2020-04-01 Panagiotis Lolas

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

Methodology · Statistics 2015-05-20 Yilun Chen , Ami Wiesel , Alfred O. Hero

A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…

Methodology · Statistics 2020-02-13 Esa Ollila , Daniel P. Palomar , Frederic Pascal

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…

Statistical Finance · Quantitative Finance 2023-04-19 Taras Bodnar , Nestor Parolya , Wolfgang Schmid

A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues…

Methodology · Statistics 2020-10-29 Esa Ollila , Daniel P. Palomar , Frédéric Pascal

The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a…

Statistics Theory · Mathematics 2020-10-28 Chun-Hao Yang , Hani Doss , Baba C. Vemuri

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…

Statistics Theory · Mathematics 2012-12-13 T. Tony Cai , Weidong Liu , Harrison H. Zhou

In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased…

Statistics Theory · Mathematics 2007-10-08 Hisayuki Hara

This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov…

Statistics Theory · Mathematics 2025-03-12 Benoit Oriol , Alexandre Miot

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…

Machine Learning · Statistics 2020-06-19 Weidong Liu , Xiaojun Mao , Raymond K. W. Wong

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…

Statistics Theory · Mathematics 2018-07-04 Nicolas Auguin , David Morales-Jimenez , Matthew R. McKay , Romain Couillet

Recently, in the context of covariance matrix estimation, in order to improve as well as to regularize the performance of the Tyler's estimator [1] also called the Fixed-Point Estimator (FPE) [2], a "shrinkage" fixed-point estimator has…

Applications · Statistics 2015-06-18 Frederic Pascal , Yacine Chitour , Yihui Quek

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…

Probability · Mathematics 2015-01-20 Romain Couillet , Matthew R. McKay