Estimating Quantiles of Normal Populations Under Order Restrictions

Abstract

Suppose independent random samples are drawn from k normal populations with means such that and common unknown variance σ2. Let denote the sample from the ith population i = 1, . . . ,k. In this paper simultaneous estimation of quantiles where is considered. A class of equivariant estimators is obtained and it is shown that the best equivariant estimator is minimax. For the case k = 2, a class of mixed estimators is proposed and some minimaxity results are derived. Admissible estimators are obtained within a class of minimax estimators. A new class of estimators is proposed and minimax estimators in this class are derived. Further admissible estimators within this class are obtained. A generalized Bayes estimator for the quantiles is derived. Further, some heuristic types of estimators are constructed for the quantiles. Finally the risk functions of all the proposed estimators are compared numerically