Robust statistics for test-of-independence and related structural models

This article proposes an alternative adjustment to the LR statistic which can be utilized for both of the distribution families and is derived in the context of general linear latent variate models.

Abstract

Recent research of asymptotic robustness shows that the likelihood ratio (LR) test statistic for test-of-independence based on normal theory remains valid for a general case where only independence is assumed. In contrast, under elliptical populations the LR statistic is correct if a kurtosis adjustment is made. Thus, the LR statistic itself is available for the first case, whereas a certain correction is needed for the second framework, which is seriously inconvenient for practitioners. In this article, we propose an alternative adjustment to the LR statistic which can be utilized for both of the distribution families. The theory is derived in the context of general linear latent variate models.