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We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

Statistics Theory · Mathematics 2019-12-23 Hai Shu , Bin Nan

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…

Cosmology and Nongalactic Astrophysics · Physics 2018-12-13 Alex Hall , Andy Taylor

In this work, we study the positive definiteness (PDness) problem in covariance matrix estimation. For high dimensional data, many regularized estimators are proposed under structural assumptions on the true covariance matrix including…

Methodology · Statistics 2019-04-16 Young-Geun Choi , Johan Lim , Anindya Roy , Junyong Park

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting a banded structure) or beamforming (widening the spectral null width associated with an…

Methodology · Statistics 2021-09-06 Esa Ollila , Arnaud Breloy

We consider $n$ independent $p$-dimensional Gaussian vectors with covariance matrix having Toeplitz structure. We test that these vectors have independent components against a stationary distribution with sparse Toeplitz covariance matrix,…

Statistics Theory · Mathematics 2021-02-16 Nayel Bettache , Cristina Butucea , Marianne Sorba

The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to…

Methodology · Statistics 2025-03-13 Atiq Ur Rehman , Muhammad Farooq

Multi-target linear shrinkage is an extension of the standard single-target linear shrinkage for covariance estimation. We combine several constant matrices - the targets - with the sample covariance matrix. We derive the oracle and a…

Statistics Theory · Mathematics 2025-03-13 Benoit Oriol

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

In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…

Optimization and Control · Mathematics 2024-03-01 Naqi Huang , Nestor Parolya , Theresia van Essen

In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were…

Methodology · Statistics 2019-09-04 Cheng Wang , Guangming Pan , Longbing Cao

A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…

Methodology · Statistics 2024-08-27 Stef Baas , Richard J. Boucherie , Jean-Paul Fox

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…

Statistics Theory · Mathematics 2017-05-08 Jianqing Fan , Weichen Wang , Ziwei Zhu

In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…

Methodology · Statistics 2017-04-19 B. Yuzbasi , M. Arashi , S. E. Ahmed

This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy…

Signal Processing · Electrical Eng. & Systems 2021-04-06 Lei Xie , Zishu He , Jun Tong , Jun Li , Jiangtao Xi

In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known…

Statistics Theory · Mathematics 2025-10-24 Seongmin Kim , Kwangmin Lee , Sewon Park , Jaeyong Lee

The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…

Information Theory · Computer Science 2017-09-28 Maryia Kabanava , Holger Rauhut

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…

The classic likelihood ratio test for testing the equality of two covariance matrices breakdowns due to the singularity of the sample covariance matrices when the data dimension $p$ is larger than the sample size $n$. In this paper, we…

Methodology · Statistics 2015-11-06 Tung-Lung Wu , Ping Li

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…

Machine Learning · Statistics 2018-06-08 Michael Hornstein , Roger Fan , Kerby Shedden , Shuheng Zhou