Recursive formula for E(∏i Tr{(WΣ-1)mi}), where W~Wp(∑; n) in finite and asymptotic regime
Jolanta Pielaszkiewicz, Dietrich von Rosen, Martin Singull · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2015
In this paper, we give a general recursive formula for E(∏i Tr{(WΣ-1)mi}), where W~Wp(∑; n) denotes a real Wishart matrix. Formulas for xed n; p are presented as well as asymptotic versions when n/p→c, when n,p→∞ 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.