Rank-Based Inference in Linear Models with Stable Errors

Abstract

Linear models with stable error densities are considered. The local asymptotic normality of the resulting model is established. We use this result, combined with Le~Cam's third lemma, to obtain local powers of various classical rank tests (Wilcoxon's and van der Waerden's test, the median test, and their counterparts for regression and analysis of variance) under stable laws. The same results are used to construct new rank tests achieving parametric optimality at specified stable densities. A Monte-Carlo study is conducted to compare their relative performances.