Estimating Ordered Means of a Bivariate Normal Distribution

Abstract

SYNOPTIC ABSTRACTThe problem of estimating ordered parameters arises widely in biological, agricultural, economic, and reliability experiments. Consider a bivariate normal population with unknown mean (θ1, θ2), known variances, and known correlation coefficient ρ, where θ1 ⩽ θ2. The problem of estimation of (θ1, θ2) is studied when the loss function used is sum of squared errors. We have considered two cases: equal variances and unequal variances. In both cases, a class of minimax estimators is proposed. These estimators improve upon the usual estimators. A class of admissible estimators is obtained within this class. The minimaxity and admissibility of a generalized Bayes estimator is established. Finally, the risk performance of all the proposed estimators has been compared numerically.