Diks, Cees; Tong, Howell A test for symmetries of multivariate probability distributions. (English) Zbl 0938.62062 Biometrika 86, No. 3, 605-614 (1999). Summary: A Monte Carlo test for multivariate symmetries is proposed. The Monte Carlo simulations are performed conditionally on a minimal sufficient statistic for the class of distributions with symmetric density. Additionally, a general purpose test statistic based on a distance measure between the probability density function and its symmetrised version is introduced. The Monte Carlo tests for spherical symmetry and multivariate reflection symmetry are studied numerically for this statistic and the results indicate that the tests perform well compared to other tests. The method is illustrated with an analysis of a real dataset. Cited in 13 Documents MSC: 62H15 Hypothesis testing in multivariate analysis 65C60 Computational problems in statistics (MSC2010) 65C05 Monte Carlo methods Keywords:conditional Monte Carlo test; distance-based test statistic; multivariate symmetry; significance testing PDFBibTeX XMLCite \textit{C. Diks} and \textit{H. Tong}, Biometrika 86, No. 3, 605--614 (1999; Zbl 0938.62062) Full Text: DOI