Some Optimal Selection Procedures for Dependent Normal Populations

Abstract

We consider k dependent normal populations having known equal variance. The problem is to select the population associated with the largest mean. Let π₁, ..., π_k be k populations. We assume that the random variable X_i associated with π_i (i = 1, ..., k). Let X₁, ..., X_k be k—variate normal distribution with unknown mean μ₁, ... , μ_k and with equal variance σ² and with correlation matrix {ρ_{i j}} For two case : (a) ρ_{i j} = a_ia_j for i ≠ j and (b) ρ_{i j} = ρ, for i ≠ j, we construct some optimal subset selection procedure to select a subset of the k dependent normal population containing the largest population mean.

AMS ( 1980) subject classification : Primary 62F07 ; Secondary 62030