Invariant tests for symmetry about an unspecified point based on the empirical characteristic function |
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Authors: | N Henze B Klar S G Meintanis |
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Institution: | a Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr. 2, Karlsruhe 76128, Germany;b Department of Engineering Sciences, University of Patras, 261 10, Patras, Greece |
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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. |
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Keywords: | Test for symmetry Affine invariance Mardia's measure of multivariate skewness Skewness in the sense of Mó ri Rohatgi and Szé kely Empirical characteristic function Permutational limit theorem |
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