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A class of optimal tests for symmetry based on local Edgeworth approximations

par Cassart, Delphine ;Hallin, Marc ;Paindaveine, Davy
Référence Bernoulli, 17, page (1063-1094)
Publication Publié, 2011

Article révisé par les pairs

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Résumé :

The objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding symmetry into adequate families of asymmetric (local) alternatives. We construct such families by considering non-Gaussian generalizations of classical first-order Edgeworth expansions indexed by a measure of skewness such that (i) location, scale and skewness play well-separated roles (diagonality of the corresponding information matrices), and (ii) the classical tests based on the Pearson-Fisher coefficient of skewness are optimal in the vicinity of Gaussian densities.