UMVU estimation of the ratio of powers
of normal generalized variances under correlation
George Iliopoulos
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 (2001) 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.
Key words and phrases: Multivariate normal distribution, ratio of powers of generalized variances, unbiased estimation, canonical correlations, zonal polynomials, hypergeometric function of matrix argument.