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

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

2011-08-10

arxiv.org/abs/1108.2171v1

Bernoulli 2011, Vol. 17, No. 3, 1063-1094

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ298 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ298

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.

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