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Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Machine Learning · Statistics 2021-02-03 Malik Tiomoko , Florent Bouchard , Guillaume Ginholac , Romain Couillet

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

The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…

Physics and Society · Physics 2007-05-23 Gabriel Frahm , Uwe Jaekel

In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…

Statistics Theory · Mathematics 2012-05-14 Karim Lounici

Linear shrinkage estimators of a covariance matrix --- defined by a weighted average of the sample covariance matrix and a pre-specified shrinkage target matrix --- are popular when analysing high-throughput molecular data. However, their…

Methodology · Statistics 2018-09-24 Harry Gray , Gwenaël G. R. Leday , Catalina A. Vallejos , Sylvia Richardson

We study the estimation of the high-dimensional covariance matrix andits eigenvalues under dynamic volatility models. Data under such modelshave nonlinear dependency both cross-sectionally and temporally. We firstinvestigate the empirical…

Statistics Theory · Mathematics 2022-11-22 Yi Ding , Xinghua Zheng

This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…

Methodology · Statistics 2025-02-25 Dong Li , Xinghao Qiao , Cheng Yu

This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…

Statistics Theory · Mathematics 2010-10-13 Nicolas Verzelen

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…

Methodology · Statistics 2018-02-19 Yilei Wu , Yingli Qin , Mu Zhu

Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…

Machine Learning · Statistics 2013-12-17 Majid Janzamin , Animashree Anandkumar

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

We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…

Statistics Theory · Mathematics 2020-12-04 Samprit Banerjee , Stefano Monni

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…

Computation · Statistics 2017-07-20 Tomer Lancewicki

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

The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…

Data Analysis, Statistics and Probability · Physics 2008-12-02 M. Tumminello , F. Lillo , R. N. Mantegna

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

Computation · Statistics 2022-11-02 Qian LI , Binyan Jiang , Defeng Sun

We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…

Statistics Theory · Mathematics 2024-10-23 Yunbum Kook , Matthew S. Zhang

This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…

Methodology · Statistics 2020-07-28 Yi Zhao , Brian S. Caffo , Xi Luo

In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The…

Information Theory · Computer Science 2015-10-28 Julia Vinogradova , Romain Couillet , Walid Hachem

We establish large sample approximations for an arbitray number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using $ \ell_1$-bounded and small $\ell_2$-bounded weighting vectors.…

Probability · Mathematics 2020-09-01 Ansgar Steland , Rainer von Sachs