Permutation Tests for Reflected Symmetry
The paper presents a permutation procedure for testing reflected (or diagonal) symmetry of the distribution of a multivariate variable. The test statistics are based in empirical characteristic functions. The resulting permutation tests are strictly distribution free under the null hypothesis that the underlying variables are symmetrically distributed about a center. Furthermore, the permutation tests are strictly valid if the symmetric center is known and are asymptotic valid if the center is an unknown point. The equivalence, in the large sample sense, between the tests and their permutation counterparts are established. The power behavior of the tests and their permutation counterparts under local alternative are investigated. Some simulations with small sample sizes ([less-than-or-equals, slant]20) are conducted to demonstrate how the permutation tests works.
Volume (Year): 67 (1998)
Issue (Month): 2 (November)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Baringhaus, L. & Henze, N., 1991. "Limit distributions for measures of multivariate skewness and kurtosis based on projections," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 51-69, July.
- Fang, K. T. & Zhu, L. X. & Bentler, P. M., 1993. "A Necessary Test of Goodness of Fit for Sphericity," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 34-55, April.
- David Blough, 1989. "Multivariate symmetry via projection pursuit," Annals of the Institute of Statistical Mathematics, Springer, vol. 41(3), pages 461-475, September.
- Heathcote, C. R. & Rachev, S. T. & Cheng, B., 1995. "Testing Multivariate Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 91-112, July.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:129-153. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.