Covariance matrix estimation under data-based loss

Dominique Fourdrinier, Anis M. Haddouche and Fatiha Mezoued

Statistics & Probability Letters, 2021, vol. 177, issue C

Abstract: We consider here the problem of estimating the p×p scale matrix Σ of a multivariate linear regression model when the distribution of the observed matrix belongs to a large class of elliptically symmetric distributions. Any estimator Σˆ of Σ is assessed through the data-based loss tr(S+Σ(Σ−1Σˆ−Ip)2)where S is the sample covariance matrix and S+ is its Moore–Penrose inverse.

Keywords: Data-based loss; Elliptically symmetric distributions; High-dimensional statistics; Orthogonally invariant estimators; Stein-Haff type identities (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109160

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