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

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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 *Delta* and degrees of freedom *n*_{1}
and *n*_{2}.
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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