Hodges-Lehmann optimality of tests (Q1198988)

Hodges-Lehmann efficiency is a dual of the more familiar notion of Bahadur efficiency. While optimal tests in Bahadur sense are somewhat rare there are many situations in which optimal tests in Hodges-Lehmann sense can be obtained. For example, generalized Kolmogorov-Smirnov and Cramér-von Mises tests for goodness-of-fit can be shown to be \(H-L\) optimal. The paper also obtains \(H-L\) optimal tests in one-parameter exponential families for testing a composite null against a fixed alternative.