Simultaneous Estimation of Quantiles for Two Normal Populations with Common Mean and Ordered Variances with Some Real Life Applications

Abstract

Suppose there are two normal populations having common mean μ and different variances. Assuming that the variances follow a simple ordering, we estimate the quantile vector. Under order restrictions on the variances, some new estimators for the quantile vector are derived. These new estimators are shown to dominate their unrestricted counterparts in terms of the risks with respect to the quadratic loss. The percentage of risk reduction of the new estimators using prior information regarding the ordering of the variances is quite significant. Finally, some real life datasets are considered for analysis purposes