On improving the shortest length confidence interval for the generalized variance

A multivariate extension of Cohen's (1972, J. Amer. Statist. Assoc. 67 382-387) result on interval estimation of normal variance is made in this article. Based on independent random matrices X : p - m and S : p - p distributed, respectively, as Npm([mu], [Sigma] [circle times operator] Im) and Wp(n, [Sigma]) with [mu] unknown and n >= p, the problem of obtaining confidence interval for [Sigma] is considered. The shortest length invariant confidence interval is obtained and is shown to be improved by some other interval estimators. Some new properties of the noncentral and central distributions of sample generalized variance have been proved for this purpose.