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.Comment: 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
