Statistica Sinica 27 (2017), 1793-1813
Abstract: This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of the test statistic, we demonstrate its robustness analytically and numerically, and investigate the properties of its influence function and breakdown point. A proposed method to select the tuning parameter q offers a good efficiency/robustness trade-off compared with the traditional likelihood ratio test (LRT) and other robust tests. Simulation and a real data analysis provide further evidence of the advantages of the proposed LqRT method. In particular, for the special case of testing the location parameter in the presence of gross error contamination, the LqRT dominates the Wilcoxon-Mann-Whitney test and the sign test at various levels of contamination.
Key words and phrases: Gross error model, relative efficiency, robustness.