On rules based on sample medians for selection of the largest location parameter

Abstract

The problem of selection of a subset containing the largest of several location parameters is considered, and a Gupta-type selection rule based on sample medians is investigated for normal and double exponential populations. Numerical comparisons between rules based on medians and means of small samples are made for normal and contaminated normal populations, assuming the popula-tion means to be equally spaced. It appears that the rule based on sample means loses its superiority over the rule based on sample medians in case the samples are heavily contaminated. The asymptotic relative efficiency (ARE) of the medians procedure relative to the means procedure is also computed, assuming the normal means to be in a slippage configuration. The means proce-dure is found to be superior to the median procedure in the sense of ARE. As in the small sample case, the situation is reversed if the normal populations are highly contaminate.