(Received January 9, 1989; revised July 23, 1990)
Abstract. Let Fp × p have the multivariate F-distribution with a scale matrix Delta and degrees of freedom n1 and n2. In this paper the problem of estimating eigenvalues of Delta is considered. By constructing the improved orthogonally invariant estimators ^Delta(F) of Delta, which are analogous to Haff-type estimators of a normal covariance matrix, new estimators of eigenvalues of Delta are given. This is because the eigenvalues of ^Delta(F) are taken as estimates of the eigenvalues of Delta.
Key words and phrases: Estimation of eigenvalues, multivariate F-distribution, covariance matrix, orthogonally invariant estimators.
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