Estimation of the eigenvalues of noncentrality parameter matrix in noncentral Wishart distribution

Abstract

We consider the problem of estimating the eigenvalues of noncentrality parameter matrix in noncentral Wishart distribution when the scale parameter is known. A decision theoretic approach is taken with squared error as the loss function. We propose two new estimators and show their superior performance to an usual estimator theoretically and numerically. r

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

“…For some of these studies, see Fujikosih and Isogai [43], Fujikoshi and Ochi [53], Siotani and Fujikoshi [99], Fujikoshi and Nishii [50], Fujikoshi et al [48], Kariya et al [80], Fujikoshi and Watamori [64], Otake et al [86], Fujikoshi [31], Seo et al [96], Naito et al [85], Kanda and Fujikoshi [77], Gupta et al [68], etc. At the time of his retirement of Hiroshima University, the number of published papers written by Professor Fujikoshi was 124, and after retirement, he has written another eight papers.…”

Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices

“…Prominent examples include wireless communication systems [7,25,26,39,41,50,53], synthetic aperture radar (SAR) signal processing [32], econometrics [51], statistical physics [4,55], and multivariate statistical analysis [9,21,23,48]. In many cases, the Wishart matrices of interest are complex [18], correlated, and non-central.…”