Least Favorable Parameter Configurations for a Step-down Subset Selection Procedure

Abstract

Given a k-dimensional vector X, k≥2, the range-type statistic with J⊆I≡{1, …, k}, plays an important role in stepwise subset selection as well as in testing whether a<?tlb> prespecified subset of k populations exclusively consists of good ones. Although in previous papers least favorable parameter configurations (LFC's) for this statistic, which are worth knowing for the calculations of critical values, have been already shown to be from a small finite subset of the parameter space, further reduction has been conjectured. Under the assumption of a log-concave and symmetric Lebesgue density with shift parameter, it is proved that in many cases the LFC can be uniquely given or, at least, found among only a few candidates. The resulting step-down selection procedure will be illustrated for data from a balanced incomplete block design.