Estimation of the inverse scatter matrix of an elliptically symmetric distribution

Dominique Fourdrinier, Fatiha Mezoued and Martin T. Wells

Journal of Multivariate Analysis, 2016, vol. 143, issue C, 32-55

Abstract: We consider estimation of the inverse scatter matrices Σ−1 for high-dimensional elliptically symmetric distributions. In high-dimensional settings the sample covariance matrix S may be singular. Depending on the singularity of S, natural estimators of Σ−1 are of the form aS−1 or aS+ where a is a positive constant and S−1 and S+ are, respectively, the inverse and the Moore–Penrose inverse of S. We propose a unified estimation approach for these two cases and provide improved estimators under the quadratic loss tr(Σˆ−1−Σ−1)2. To this end, a new and general Stein–Haff identity is derived for the high-dimensional elliptically symmetric distribution setting.

Keywords: Elliptically symmetric distributions; High-dimensional statistics; Moore–Penrose inverse; Inverse scatter matrix; Quadratic loss; Singular sample covariance matrix; Sample eigenvalues; Stein–Haff identity (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2015.08.012

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