IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v67y1998i2p129-153.html
   My bibliography  Save this article

Permutation Tests for Reflected Symmetry

Author

Listed:
  • Neuhaus, Georg
  • Zhu, Li-Xing

Abstract

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.

Suggested Citation

  • Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
  • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:129-153
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91697-3
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Heathcote, C. R. & Rachev, S. T. & Cheng, B., 1995. "Testing Multivariate Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 91-112, July.
    4. David Blough, 1989. "Multivariate symmetry via projection pursuit," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 461-475, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christian Genest & Johanna NeŇ°lehov√°, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    2. Henze, N. & Klar, B. & Meintanis, S. G., 2003. "Invariant tests for symmetry about an unspecified point based on the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 275-297, November.
    3. repec:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-016-0514-2 is not listed on IDEAS
    4. Zhu, Lixing & Zhu, Ruoqing & Song, Song, 2008. "Diagnostic checking for multivariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1841-1859, October.
    5. Rainer Dyckerhoff & Christophe Ley & Davy Paindaveine, 2015. "Depth-based runs tests for bivariate central symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 917-941, October.
    6. repec:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0680-4 is not listed on IDEAS
    7. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0732-4 is not listed on IDEAS
    8. Xuehu Zhu & Xu Guo & Lu Lin & Lixing Zhu, 2016. "Testing for positive expectation dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 135-153, February.
    9. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.