Journal of Multivariate Analysis
Improving on the best affine equivariant estimator of the ratio of generalized variances
Journal of Multivariate Analysis
Descriptive measures of multivariate scatter and linear dependence
Journal of Multivariate Analysis
MOPS: Multivariate orthogonal polynomials (symbolically)
Journal of Symbolic Computation
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We consider estimation of the ratio of arbitrary powers of two normal generalized variances based on two correlated random samples. First, the result of Iliopoulos [Decision theoretic estimation of the ratio of variances in a bivariate normal distribution, Ann. Inst. Statist. Math. 53 (2001) 436-446] on UMVU estimation of the ratio of variances in a bivariate normal distribution is extended to the case of the ratio of any powers of the two variances. Motivated by these estimators' forms we derive the UMVU estimator in the multivariate case. We show that it is proportional to the ratio of the corresponding powers of the two sample generalized variances multiplied by a function of the sample canonical correlations. The mean squared errors of the derived UMVU estimator and the maximum likelihood estimator are compared via simulation for some special cases.