On estimation of the scale matrix of the multivariate f distribution

Abstract

Let F _p×phave a multivariate F distribution with a scale p×p matrix Δ and degrees of freedom k₁ and k₂ such that k_i - p - 1 > 0, i = 1,2. The estimation of Δ under entropy and squared error loss functions are considered. In both cases a new class of orthogonally invariant estimators are obtained which dominate the best unbiased estimator.

Keywords:

• Multivariate F distribution
• orthogonally invariant estimator
• entropy loss
• squared error loss
• covariance matrix