AISM 53, 436-446

© 2001 ISM

## Decision theoretic estimation of the ratio of variances in a bivariate
normal distribution

### George Iliopoulos

Department of Mathematics,
University of Patras, 26500 Rio, Patras, Greece

(Received May 6, 1999; revised March 1, 2000)

Abstract.
In this paper the problem of estimating the ratio of
variances,
$\sigma$, in a bivariate normal distribution with unknown mean is
considered from a decision-theoretic point of view. First, the UMVU
estimator of $\sigma$ 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.

Key words and phrases:
Decision theory, bivariate normal
distribution, ratio of variances, squared error loss, entropy loss.

**Source**
(TeX, DVI )