More good news on the HKM test for multivariate reflected symmetry about an unknown centre

Autor: Celeste Mayer, Norbert Henze
Rok vydání: 2019
Předmět:
Zdroj: Annals of the Institute of Statistical Mathematics. 72:741-770
ISSN: 1572-9052
0020-3157
DOI: 10.1007/s10463-019-00707-5
Popis: We revisit the problem of testing for multivariate reflected symmetry about an unspecified point. Although this testing problem is invariant with respect to full-rank affine transformations, among the few hitherto proposed tests only a class of tests studied in Henze et al. (J Multivar Anal 87:275–297, 2003) that depends on a positive parameter a respects this property. We identify a measure of deviation $$\varDelta _a$$ (say) from symmetry associated with the test statistic $$T_{n,a}$$ (say), and we obtain the limit normal distribution of $$T_{n,a}$$ as $$n \rightarrow \infty $$ under a fixed alternative to symmetry. Since a consistent estimator of the variance of this limit normal distribution is available, we obtain an asymptotic confidence interval for $$\varDelta _a$$. The test, when applied to a classical data set, strongly rejects the hypothesis of reflected symmetry, although other tests even do not object against the much stronger hypothesis of elliptical symmetry.
Databáze: OpenAIRE
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