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Testing for symmetry in multivariate distributions. (English) Zbl 1463.62171

Summary: Using the empirical characteristic function, a Cramér-von Mises test for reflected symmetry about an unspecified point is derived for multivariate distributions. The test statistic is based on an empirical process for which the weak convergence is established. The null properties of the test are studied as well as its power and local power. Estimators for the unknown symmetric point are previously proposed. Their consistency and asymptotical normality are proved by studying the weak convergence of some multidimensional empirical process. A simulation experiment shows that the estimators of the symmetric point are good, and that the test performs well on the examples tested. The new test is compared to the one derived in [N. Henze et al., J. Multivariate Anal. 87, No. 2, 275–297 (2003; Zbl 1040.62047)].

MSC:

62H15 Hypothesis testing in multivariate analysis
62G30 Order statistics; empirical distribution functions
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 1040.62047
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References:

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