On E [Pi(k)(i=0) Tr{W-mi}], where W similar to Wp (l, n)

Abstract

In this paper, we give a general recursive formula for [Pi(k)(i=0) Tr{W-mi}], where W similar to Wp (l, n) denotes a real Wishart matrix. Formulas for fixed n, p are presented as well as asymptotic versions when n/p (n,p ->infinity) -> c, i.e., when the so called Kolmogorov condition holds. Finally, we show application of the asymptotic moment relation when deriving moments for the Marchenko-Pastur distribution (free Poisson law). A numerical illustration using implementation of the main result is also performed.

Keywords

Eigenvalue distribution; free moments; free Poisson law; Marchenko-Pastur law; random matrices; spectral distribution; Wishart matrix

Published in

Communications in Statistics - Theory and Methods
2017, volume: 46, number: 6, pages: 2990-3005
Publisher: TAYLOR & FRANCIS INC

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    
  • Linköping University

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1080/03610926.2015.1053942

Permanent link to this page (URI)

https://res.slu.se/id/publ/94149