Robust Hypothesis Testing via Lq-Likelihood

TL;DR

This paper proposes a new robust hypothesis testing method called Lq-likelihood-ratio-type test (LqRT), which offers improved robustness and efficiency over traditional tests, demonstrated through theoretical analysis and empirical validation.

Contribution

The paper introduces the LqRT, a novel robust hypothesis testing procedure with a data-driven method for selecting the tuning parameter q, enhancing robustness and efficiency.

Findings

LqRT has a well-defined asymptotic distribution.

LqRT outperforms traditional tests under data contamination.

LqRT is more effective than Wilcoxon-Mann-Whitney and sign tests in contaminated settings.

Abstract

This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and numerically, and they investigate the properties of both its influence function and its 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. A simulation and real data analysis provides 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.