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Research article2018Peer reviewedOpen access

On n/p-Asymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrices

Pielaszkiewicz, Jolanta; von Rosen, Dietrich; Singull, Martin

Abstract

The joint distribution of standardized traces of 1/n XX' and of (1/n XX')(2), where the matrix X : p x n follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition n/p ->(n,p ->infinity) c> 0. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of n and p.

Keywords

Wishart matrix; Multivariate normal distribution; Spectral distribution; Spectral moments; Covariance matrix

Published in

Electronic Journal Of Linear Algebra
2018, Volume: 33, pages: 24-40
Publisher: INT LINEAR ALGEBRA SOC

    UKÄ Subject classification

    Algebra and Logic

    Publication identifier

    DOI: https://doi.org/10.13001/1081-3810.3732

    Permanent link to this page (URI)

    https://res.slu.se/id/publ/112436