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August 2011 A class of optimal tests for symmetry based on local Edgeworth approximations
Delphine Cassart, Marc Hallin, Davy Paindaveine
Bernoulli 17(3): 1063-1094 (August 2011). DOI: 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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Delphine Cassart. Marc Hallin. Davy Paindaveine. "A class of optimal tests for symmetry based on local Edgeworth approximations." Bernoulli 17 (3) 1063 - 1094, August 2011.


Published: August 2011
First available in Project Euclid: 7 July 2011

zbMATH: 1221.62068
MathSciNet: MR2817618
Digital Object Identifier: 10.3150/10-BEJ298

Keywords: Edgeworth expansion , local asymptotic normality , locally asymptotically most powerful tests , skewed densities , tests for symmetry

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability


Vol.17 • No. 3 • August 2011
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