A test for symmetries of multivariate probability distributions

被引:21
作者
Diks, C
Tong, H
机构
[1] Univ Amsterdam, Dept Econ, NL-1018 WB Amsterdam, Netherlands
[2] Univ Hong Kong, Dept Stat, Pokfulam, Peoples R China
基金
英国工程与自然科学研究理事会;
关键词
conditional Monte Carlo test; distance-based test statistic; multivariate symmetry; significance testing;
D O I
10.1093/biomet/86.3.605
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
引用
收藏
页码:605 / 614
页数:10
相关论文
共 31 条
[21]  
LOCKHART RA, 1985, BIOMETRIKA, V85, P208
[22]  
Marriott F. H. C., 1979, Applied Statistics, V28, P75
[23]   Permutation tests for reflected symmetry [J].
Neuhaus, G ;
Zhu, LX .
JOURNAL OF MULTIVARIATE ANALYSIS, 1998, 67 (02) :129-153
[24]   CRAMER VON-MISES TYPE STATISTIC FOR TESTING SYMMETRY [J].
ROTHMAN, ED ;
WOODROOFE, M .
ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (06) :2035-2038
[25]  
SCHACH S, 1969, BIOMETRIKA, V56, P571
[26]  
Serfling R.J., 1980, APPROXIMATION THEORE
[27]  
SMALL NJH, 1980, APPLIED STATISTICS, V29, P85, DOI DOI 10.2307/2346414
[28]   CRAMERVONMISES TYPE STATISTIC FOR TESTING SYMMETRY [J].
SRINIVAS.R ;
GODIO, LB .
BIOMETRIKA, 1974, 61 (01) :196-198
[29]  
Wijsman R.A., 1990, Lecture Notes-Monograph Series, V14
[30]  
ZHU LX, 1995, PAKISTAN J STAT, V11, P49