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Related papers: Covariance Estimation for Matrix-valued Data

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We propose a Kronecker product model for correlation or covariance matrices in the large dimensional case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD)…

Statistics Theory · Mathematics 2019-05-20 Christian M. Hafner , Oliver B. Linton , Haihan Tang

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance…

Methodology · Statistics 2013-10-11 Kristjan Greenewald , Theodoros Tsiligkaridis , Alfred O Hero

Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral…

Statistics Theory · Mathematics 2022-05-02 Long Yu , Jiahui Xie , Wang Zhou

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…

Image and Video Processing · Electrical Eng. & Systems 2022-07-27 Jonathan Monsalve , Juan Ramirez , Iñaki Esnaola , Henry Arguello

The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution…

Portfolio Management · Quantitative Finance 2021-01-08 Sven Husmann , Antoniya Shivarova , Rick Steinert

In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…

Probability · Mathematics 2010-10-05 Thomas L. Marzetta , Gabriel H. Tucci , Steven H. Simon

Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong…

Methodology · Statistics 2024-12-05 Yifan Yang , Chixiang Chen , Shuo Chen

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

Multiway data analysis aims to uncover patterns in data structured as multi-indexed arrays, with multiway covariance playing a crucial role in many applications. However, the high dimensionality of multiway covariance presents significant…

Statistics Theory · Mathematics 2026-03-19 Dogyoon Song , Alfred O. Hero

We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…

Statistics Theory · Mathematics 2018-01-17 Stanislav Minsker , Xiaohan Wei

This paper proposes methods for likelihood-based inference in multivariate linear regressions when the correlation matrix of the responses is separable; that is, it has a Kronecker product structure, but the variances are unrestricted. The…

Computation · Statistics 2026-04-16 Karl Oskar Ekvall

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Methodology · Statistics 2025-12-30 Shaoxin Wang , Ziyun Ma

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

Econometrics · Economics 2019-10-29 Jaeheon Jung

We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…

Methodology · Statistics 2022-02-08 Elias Raninen , David E. Tyler , Esa Ollila

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

We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…

Information Theory · Computer Science 2022-04-25 Sjoerd Dirksen , Johannes Maly , Holger Rauhut

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 the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Robotics · Computer Science 2023-09-19 Mohamad Qadri , Zachary Manchester , Michael Kaess

The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…

Methodology · Statistics 2024-11-12 Philippe Boileau , Nima S. Hejazi , Mark J. van der Laan , Sandrine Dudoit

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