A class of optimal tests for symmetry based on local Edgeworth approximations
Abstract
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.
Keywords
Cite
@article{arxiv.1108.2171,
title = {A class of optimal tests for symmetry based on local Edgeworth approximations},
author = {Delphine Cassart and Marc Hallin and Davy Paindaveine},
journal= {arXiv preprint arXiv:1108.2171},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.3150/10-BEJ298 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)