Robust Testing of the Nonparametric Behrens-Fisher Hypothesis Using a Density Ratio Model

• Activity Number: 508
• Type: Contributed
• Date/Time: Thursday, August 10, 2006 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): James Troendle*+ and Kostas Fokianos
• Companies: National Institute of Child Health & Human Development and University of Cyprus
• Keywords: Box-Cox transformation ; empirical likelihood ; likelihood ratio test ; Mann-Whitney-Wilcoxon test ; power ; simulation

Abstract

Consider the problem of comparing two populations based on a random sample from each distribution, without making any distributional assumptions. A common formulation of this problem is known as the nonparametric Behrens--Fisher problem. To obtain a robust test, we assume a density ratio model holds for a suitable Box--Cox transformation of the data. The transformation, along with the density ratio model, is estimated by maximum empirical likelihood. A new test procedure is developed specifically for testing the nonparametric Behrens-Fisher hypothesis within this framework and its performance is examined by simulations, and on birthweight data of Nulliparous women in spontaneous labor. The test is compared with some nonparametric competitors, and it is found to have relatively high power across a wide variety of distributions including those outside of the density ratio family.