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, σ, in a bivariate normal distribution with unknown mean is considered from a decision– theoretic point of view. First, the UMVU estimator of σ 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.