Rank based testing in linear models with stable errors
Hallin, Marc Swan, Yvik Verdebout, Thomas Veredas, David
Hallin, Marc
Swan, Yvik
Verdebout, Thomas
Veredas, David
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Publication Type
Journal article
Editor
Supervisor
Publication Year
2011
Journal
Journal of Nonparametric Statistics
Book
Publication Volume
23
Publication Issue
2
Publication Begin page
305
Publication End page
320
Publication Number of pages
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Abstract
Linear models with stable error densities are considered, and their local asymptotic normality with respect to the regression parameter is established. We use this result, combined with Le Cam's third lemma, to obtain local powers and asymptotic relative efficiencies for various classical rank tests (the regression and analysis of variance counterparts of the Wilcoxon, van der Waerden and median tests) under α-stable densities with various values of the skewness parameter and tail index. The same results are used to construct new rank tests, based on ‘stable scores’, achieving parametric optimality at specified stable densities. A Monte Carlo study is conducted to compare their finite-sample relative performances.
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Accounting & Finance