Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions

Asymmetry models; Local asymptotic normality; Location tests; Rank-based inference; Tests of symmetry; Statistics and Probability; Statistics, Probability and Uncertainty

Abstract :

[en] When testing symmetry of a univariate density, (parametric classes of) densities skewed by means of the general probability transform introduced in Ferreira and Steel [A constructive representation of univariate skewed distributions, J. Amer. Statist. Assoc. 101 (2006), pp. 823-829] are appealing alternatives. This paper first proposes parametric tests of symmetry (about a specified centre) that are locally and asymptotically optimal (in the Le Cam sense) against such alternatives. To improve on these parametric tests, which are valid under well-specified density types only, we turn them into semiparametric tests, either by using a standard studentisation approach or by resorting to the invariance principle. The second approach leads to robust yet efficient signed-rank tests, which include the celebrated sign and Wilcoxon tests as special cases, and turn out to be Le Cam optimal irrespective of the underlying original symmetric density. Optimality, however, is only achieved under well-specified 'skewing mechanisms', and we therefore evaluate the overall performances of our tests by deriving their asymptotic relative efficiencies with respect to the classical test of skewness. A Monte-Carlo study confirms the asymptotic results. © 2009 Taylor & Francis.

Disciplines :

Mathematics

Author, co-author :

LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Universit́ Libre de Bruxelles, E.C.A.R.E.S., Institut de Recherche en Statistique, D́partement de Math́matique, Brussels, Belgium

Paindaveine, Davy; Universit́ Libre de Bruxelles, E.C.A.R.E.S., Institut de Recherche en Statistique, D́partement de Math́matique, Brussels, Belgium

External co-authors :

yes

Language :

English

Title :

Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions

Publication date :

November 2009

Journal title :

Journal of Nonparametric Statistics

ISSN :

1048-5252

eISSN :

1029-0311

Publisher :

Informa UK Limited

Volume :

Issue :

Pages :

943 - 967

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://www.tandfonline.com/doi/pdf/10.1080/10485250902971765

Funding text :

Christophe Ley thanks the Fonds National de la Recherche Scientifique, Communauté française de Belgique, for support via a Mandat d’Aspirant FNRS. Davy Paindaveine is grateful to the Fonds National de la Recherche Scientifique, Communauté française de Belgique, for a Mandat d’Impulsion Scientifique. The authors would like to thank the editor, the associate editor, and an anonymous referee for their valuable comments that helped them improve significantly the quality of the paper. Davy Paindaveine is a member of ECORE, the recently created association between CORE and ECARES.

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