Sammanfattning

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.

Nyckelord

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

Publicerad i

Communications in Statistics - Theory and Methods
2017, Volym: 46, nummer: 6, sidor: 2990-3005
Utgivare: TAYLOR & FRANCIS INC

SLU författare

• von Rosen, Dietrich

  • Institutionen för energi och teknik, Sveriges lantbruksuniversitet
    
  • Linköpings universitet

UKÄ forskningsämne

Sannolikhetsteori och statistik


Publikationens identifierare

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

Permanent länk till denna sida (URI)

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