Influence functions for rank-based procedures in the linear model

Abstract

Throughout the development of rank-based methods, the influence function has often been ignored. In this paper, we give the influence functions for the scores rank estimate and the corresponding drop test (based on the difference in dispersion between the full and reduced fits). We show how the influence function measures resistance of the estimator to contamination and how proper score selection leads to more resistant procedures. Furthermore, the asymptotic distribution of the estimator and test can be inferred from the influence function. We also introduce the drop test statistic for the weighted rank-based procedure of Naranjo and Hettmansperger. This test statistic has an influence function that is bounded in both x and y space, and reduces to the regular rank dispersion test using Wilcoxon scores in the unweighted case.