A NOTE ON ESTIMATING EIGENVALUES OF SCALE MATRIX OF THE MULTIVARIATE F-DISTRIBUTION

YOSHIHIKO KONNO

Faculty of Business Administration, Ishinomaki Senshu University, Ishinomaki, Miyagi 986, Japan

(Received January 9, 1989; revised July 23, 1990)

Abstract. Let F_{p×p} have the multivariate F-distribution with a scale matrix Δ and degrees of freedom n_{1} and n_{2}. In this paper the problem of estimating eigenvalues of Δ is considered. By constructing the improved orthogonally invariant estimators Δ̂(F) of Δ, which are analogous to Haff-type estimators of a normal covariance matrix, new estimators of eigenvalues of Δ are given. This is because the eigenvalues of Δ̂(F) are taken as estimates of the eigenvalues of Δ.

Key words and phrases: Estimation of eigenvalues, multivariate F-distribution, covariance matrix, orthogonally invariant estimators.