Invariant tests for symmetry about an unspecified point based on the empirical characteristic function

Authors:
N. Henze;B. Klar;S. G. Meintanis
Affiliations:
Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr. 2, Karlsruhe 76128, Germany;Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr. 2, Karlsruhe 76128, Germany;Department of Engineering Sciences, University of Patras, 261 10 Patras, Greece
Venue:
Journal of Multivariate Analysis
Year:
2003

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Abstract

This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably standardized given data, and they have an alternative representation in terms of an L2-distance of nonparametric kernel density estimators. Moreover, there is a connection with two measures of multivariate skewness. The tests are performed via a permutational procedure that conditions on the data.