ESTIMATION OF ORDERED LOCATION PARAMETERS - THE EXPONENTIAL-DISTRIBUTION

The problem of component wise estimation of ordered location parameters theta1 and theta2 (theta1 less-than-or-equal-to theta2) of two independent exponential distributions is investigated. The scale parameters are assumed to be unequal but known. Independent random samples of unequal sample sizes are drawn from two populations and the estimators admissible among the mixed estimators of theta1 and theta2 are obtained. It is shown that the minimum risk estimators (MREs) of theta1 and theta2 without assuming theta1 less-than-or-equal-to theta2 are inadmissible when one does assume that theta1 less-than-or-equal-to theta2. The efficiencies of mixed estimators relative to MREs (without assuming theta1 less-than-or-equal-to theta2) are tabulated for equal sample sizes and equal scale parameters. AMS 1980 subject classification: Primary 62G05; secondary 62N05.