Estimating Quantile of the Selected Normal Population

Suppose independent random samples are available from two normal populations with same mean and different variances where both are unknown. The population corresponding to the smallest sum of the squared deviations from the mean is selected as the best population. We consider estimation of quantiles of the selected population. Some estimators are proposed. Admissible class of estimators for the quantile of the selected population is found in certain subclasses of estimators. The biases and mean squared error risks of the proposed estimators are compared numerically by Monte-Carlo simulation.