Rank-Based Inference in Linear Models with Stable Errors

24 Pages Posted: 3 Jun 2010

See all articles by Marc Hallin

Marc Hallin

ECARES, Universite Libre de Bruxelles

Yvik Swan

Université Libre de Bruxelles (ULB) - Department of Mathematics

Thomas Verdebout

University of Lille III - EQUIPPE-GREMARS

David Veredas

Vlerick Business School

Date Written: June 1, 2010

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.

Keywords: Stable distributions, local asymptotic normality, rank tests, asymptotic relative efficiencies

Suggested Citation

Hallin, Marc and Swan, Yvik and Verdebout, Thomas and Veredas, David, Rank-Based Inference in Linear Models with Stable Errors (June 1, 2010). Available at SSRN: https://ssrn.com/abstract=1618759 or http://dx.doi.org/10.2139/ssrn.1618759

Marc Hallin

ECARES, Universite Libre de Bruxelles ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium
+32 2 650 5886 (Phone)
+32 2 650 5899 (Fax)

Yvik Swan

Université Libre de Bruxelles (ULB) - Department of Mathematics ( email )

Brussels
Belgium

Thomas Verdebout

University of Lille III - EQUIPPE-GREMARS ( email )

Lille
France

David Veredas (Contact Author)

Vlerick Business School ( email )

Library
REEP 1
Gent, BE-9000
Belgium

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