Decision theoretic estimation of the ratio of
variances
in a bivariate normal distribution
George Iliopoulos
In this paper the problem of estimating the ratio of variances, $\s$, in a
bivariate normal distribution with unknown mean is considered from a
decision--theoretic point of view. First, the UMVU estimator of $\s$ is
derived, and then it is shown to be inadmissible under two specific loss
functions, namely, the squared error loss and the entropy loss. The derivation
of the results is done by conditioning on an auxiliary negative binomial random
variable.
AMS 1991 subject classifications: 62C99, 62H12, 62F10.
Key words and phrases: Decision theory, bivariate normal distribution,
ratio of variances, squared error loss, entropy loss.