### SANAT K. SARKAR

Department of Statistics, Temple University, Philadelphia, PA 19122, U.S.A.

(Received October 24, 1989; revised March 19, 1990)

Abstract.    Based on independent random matices X: p × m and S: p × p distributed, respectively, as Npm(mu, Sigma \otimes Im) and Wp(n, Sigma) with mu unknown and n > p, the problem of obtaining confidence interval for |Sigma| is considered. Stein's idea of improving the best affine equivariant point estimator of |Sigma| has been adapted to the interval estimation problem. It is shown that an interval estimator of the form |S|(b-1, a-1) can be improved by min{|S|, c|S + XX'|}(b-1, a-1) for a certain constant c depending on (a, b).

Key words and phrases:    Generalized variance, invariant interval estimators, Stein-type improvements.

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