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Related papers: Linear pooling of sample covariance matrices

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High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases.…

Statistics Theory · Mathematics 2007-06-13 Jianqing Fan , Yingying Fan , Jinchi Lv

We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the…

Computation · Statistics 2018-09-13 Alexander Litvinenko , Ying Sun , Marc G. Genton , David Keyes

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

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…

Methodology · Statistics 2022-04-20 Yichi Zhang , Weining Shen , Dehan Kong

Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…

Methodology · Statistics 2014-08-06 Eric C. Chi , Kenneth Lange

Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…

Instrumentation and Methods for Astrophysics · Physics 2015-06-22 Rutger van Haasteren , Michele Vallisneri

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…

Machine Learning · Statistics 2015-11-23 Ilya Soloveychik , Ami Wiesel

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…

Statistics Theory · Mathematics 2016-04-20 Ilya Soloveychik , Ami Wiesel

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

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and…

Machine Learning · Statistics 2011-12-08 Noah Simon , Rob Tibshirani

This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a…

Methodology · Statistics 2019-05-22 Esa Ollila , Elias Raninen

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…

Information Theory · Computer Science 2015-06-03 Jianfeng Yao , Abla Kammoun , Jamal Najim

A classical approach to accurately estimating the covariance matrix \Sigma of a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. However, many modern applications operate with much smaller…

Statistics Theory · Mathematics 2014-03-05 Elizaveta Levina , Roman Vershynin

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…

Information Theory · Computer Science 2019-03-19 Wei Cui , Xu Zhang , Yulong Liu

The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance.…

Probability · Mathematics 2018-12-24 Gabriel H. Tucci , Ke Wang

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

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

Statistics Theory · Mathematics 2011-12-01 Parikshit Shah , Venkat Chandrasekaran

In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…

Statistics Theory · Mathematics 2011-10-26 Jérémie Bigot , Rolando Biscay , Jean-Michel Loubes , Lilian Muniz Alvarez

This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from…

Machine Learning · Statistics 2017-05-01 Farhad Pourkamali-Anaraki

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