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The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic…

High Energy Physics - Experiment · Physics 2007-05-23 Alekhin Sergey

Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm. To be specific, let $\hat\Sigma$ denote the sample…

Statistics Theory · Mathematics 2019-09-16 Miles E. Lopes , N. Benjamin Erichson , Michael W. Mahoney

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

Statistics Theory · Mathematics 2020-03-09 Rémy Mariétan , Stephan Morgenthaler

We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…

Statistics Theory · Mathematics 2025-07-29 Christian Borgs , Jennifer Chayes , Devavrat Shah , Christina Lee Yu

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

Statistics Theory · Mathematics 2008-06-26 Adam J. Rothman , Peter J. Bickel , Elizaveta Levina , Ji Zhu

We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…

Statistics Theory · Mathematics 2018-03-28 Denis Belomestny , Mathias Trabs , Alexandre B. Tsybakov

We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…

Statistics Theory · Mathematics 2015-09-09 Didier Chételat , Martin T. Wells

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…

Methodology · Statistics 2021-08-17 Shev Macnamara , Erik Schlögl , Zdravko I. Botev

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…

Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly…

Statistics Theory · Mathematics 2012-07-24 Olivier Ledoit , Michael Wolf

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…

Methodology · Statistics 2016-05-17 T. Tony Cai , Anru Zhang

Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…

Applications · Statistics 2011-12-01 Nicholas Arcolano , Patrick J. Wolfe

This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…

Statistics Theory · Mathematics 2025-07-01 Omar Al-Ghattas , Jiaheng Chen , Daniel Sanz-Alonso , Nathan Waniorek

High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…

Methodology · Statistics 2016-06-28 Sang-Yun Oh , Bala Rajaratnam , Joong-Ho Won

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…

Methodology · Statistics 2026-03-03 Rakheon Kim , Irina Gaynanova

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…

Methodology · Statistics 2011-02-14 Tony Cai , Weidong Liu

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Statistics Theory · Mathematics 2024-04-03 Jinyuan Chang , Qiao Hu , Cheng Liu , Cheng Yong Tang

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

Statistics Theory · Mathematics 2021-06-17 Eduardo Pavez , Antonio Ortega

In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…

Methodology · Statistics 2016-10-04 Jesús Arroyo , Elizabeth Hou