A Monte Carlo Study of Robustness of Preliminary Test Estimators in Pooling Means

Abstract

**Please note that the full text is embargoed** ABSTRACT: Pooling data, when justified, for estimating the target mean is advantageous when the sample size is small from the target population. In case it is doubtful whether two sets of data have the same mean, a normal test or a t test can be used for testing the equality of the two means depending on variance known or unknown. A preliminary test estimator is then constructed for estimating the population mean. We study the robustness of the preliminary test estimators when certain populations are not normal. The result of a Monte Carlo study is given, when the populations are either uniform or exponential. The relative efficiencies of the preliminary test estimators are studied. It is found that the preliminary test estimators are quite robust.