Recursive formula for E(∏i Tr{(WΣ-1)mi}), where W~Wp(∑; n) in finite and asymptotic regime

Abstract

In this paper, we give a general  recursive  formula  forE[∏ki=0Tr{Wmi}], whereW∼ Wp(I,n) denotes a real Wishart matrix. Formulas for fixed n,pare presented as well as asymptotic versions when npn,p→∞→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

Published in

LiTH-MAT-R
2015, number: 2015/04
Publisher: Linköping University

SLU Authors

• von Rosen, Dietrich

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

UKÄ Subject classification

Probability Theory and Statistics

Permanent link to this page (URI)

https://res.slu.se/id/publ/88342