Data-driven Percentile Modified Wilcoxon Tests and Their Recomposition

• Activity Number: 110
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Olivier Thas*+ and Jean-Pierre Ottoy
• Companies: Ghent University and Ghent University
• Keywords: changepoint ; symmetry ; two-sample problem ; Wilcoxon rank sum ; rank test ; Pearson statistic

Abstract

The two-sample Wilcoxon rank sum statistic can be derived as the first component of the Pearson chi-squared statistic in a particularly constructed contingency table. For this test a "percentile modification" has been proposed, which is equivalent to splitting the contingency table into two independent subtables, and computing the Wilcoxon statistic on one of the subtables. Although this procedure does not use all data in the sample, it often results in a power increase. The splitting position is determined by an arbitrarily chosen trimming proportion p. To circumvent this problem, we propose a new test statistic by using a data-dependent choice for p. We show that its asymptotic null distribution is the supremum of a time-transformed Brownian Motion. We consider two applications of the Wilcoxon statistic: testing for symmetry and the two-sample problem. In a simulation study it is shown that our solution often results in a power advantage. Also, instead of using only one subtable, we suggest to compute the Wilcoxon statistic on both subtables, and to consider their sum as a new test statistic, which we consider as a recomposition of statistics, rather than a decomposition.