Robust Hypothesis Testing via Lq-Likelihood

• Activity Number: 186
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Statistics in Business Schools Interest Group
• Author(s): Yichen Qin* and Carey E. Priebe
• Companies: University of Cincinnati Lindner College of Business and The Johns Hopkins University
• Keywords: relative efficiency ; robustness ; gross error model

Abstract

In this article, we introduce a robust testing procedure: the Lq-likelihood ratio test. We derive the asymptotic distribution of our test statistic and demonstrate its robustness properties both analytically and numerically. We further investigate the properties of its influence function and breakdown point. We also propose a method for selecting the tuning parameter q, and demonstrate that, with the q selected using our approach, our test attains an excellent efficiency/robustness trade-off compared to the traditional likelihood ratio test and other robust tests. For the special case of testing the location parameter in the presence of gross error contamination, we show that out test dominates the Wilcoxon-Mann-Whitney test and the sign test at different levels of contamination.