Optimal rank tests for symmetry against Edgeworth-type alternatives

We are constructing, for the problem of univariate symmetry (with respect to specified or unspecified location), a class of signed-rank tests achieving optimality against the family of asymmetric (local) alternatives considered in Cassart et al. (Bernoulli 17:1063–1094, 2011). Those alternatives are based on a non-Gaussian generalization of classical first-order Edgeworth expansions indexed by a measure of skewness such that (1) location, scale, and skewness play well-separated roles (diagonality of the corresponding information matrices), and (2) the classical tests based on the Pearson-Fisher coefficient of skewness are optimal in the vicinity of Gaussian densities. Asymptotic distributions are derived under the null and under local alternatives. Asymptotic relative efficiencies are computed and, in most cases, indicate that the proposed rank tests significantly outperform their traditional competitors.SCOPUS: ch.b