Pairwise versus joint ranking: Another look at the Kruskal-Wallis statistic

Abstract

A test statistic for the k -sample location problem is constructed by appropriately combining all pairwise two-sample Wilcoxon tests. The result is an analogue of the Kruskal-Wallis statistic in the sense that the Pitman asymptotic relative efficiency between the two is one. However, the approximate Bahadur efficiency of the analogue relative to the Kruskal-Wallis statistic is shown to be greater than or equal to one at every alternative.