IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i1d10.1007_s00362-022-01316-w.html
   My bibliography  Save this article

Testing for diagonal symmetry based on center-outward ranking

Author

Listed:
  • Sakineh Dehghan

    (Shahid Beheshti University)

  • Mohammad Reza Faridrohani

    (Shahid Beheshti University)

  • Zahra Barzegar

    (Saman Insurance Company)

Abstract

This paper aims to propose a new class of permutation-invariant tests for diagonal symmetry around a known point based on the center-outward depth ranking. The asymptotic behavior of the proposed tests under the null distribution is derived. The performance of the proposed tests is assessed through a Monte Carlo study. The results show that the tests perform well comparing other procedures in terms of empirical sizes and empirical powers. We demonstrated that the proposed class includes the celebrated Wilcoxon signed-rank test as a special case in the univariate setting. Finally, we apply the tests to a well-known data set to illustrate the method developed in this paper.

Suggested Citation

  • Sakineh Dehghan & Mohammad Reza Faridrohani & Zahra Barzegar, 2023. "Testing for diagonal symmetry based on center-outward ranking," Statistical Papers, Springer, vol. 64(1), pages 255-283, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01316-w
    DOI: 10.1007/s00362-022-01316-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01316-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-022-01316-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. J. P. Royston, 1983. "Some Techniques for Assessing Multivarate Normality Based on the Shapiro‐Wilk W," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 121-133, June.
    2. Schott, James R., 2002. "Testing for elliptical symmetry in covariance-matrix-based analyses," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 395-404, December.
    3. Batsidis, Apostolos & Zografos, Konstantinos, 2013. "A necessary test of fit of specific elliptical distributions based on an estimator of Song’s measure," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 91-105.
    4. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    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. Sang, Yongli & Dang, Xin, 2020. "Empirical likelihood test for diagonal symmetry," Statistics & Probability Letters, Elsevier, vol. 156(C).
    7. Sakineh Dehghan & Mohammad Reza Faridrohani, 2019. "Affine invariant depth-based tests for the multivariate one-sample location problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 671-693, September.
    8. Norbert Henze & Celeste Mayer, 2020. "More good news on the HKM test for multivariate reflected symmetry about an unknown centre," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 741-770, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    2. Norbert Henze & Celeste Mayer, 2020. "More good news on the HKM test for multivariate reflected symmetry about an unknown centre," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 741-770, June.
    3. Batsidis, Apostolos & Zografos, Konstantinos, 2013. "A necessary test of fit of specific elliptical distributions based on an estimator of Song’s measure," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 91-105.
    4. Boente, Graciela & Salibián Barrera, Matías & Tyler, David E., 2014. "A characterization of elliptical distributions and some optimality properties of principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 254-264.
    5. Schott, James R., 2002. "Testing for elliptical symmetry in covariance-matrix-based analyses," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 395-404, December.
    6. Iwashita, Toshiya & Klar, Bernhard, 2014. "The joint distribution of Studentized residuals under elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 203-209.
    7. Vexler, Albert & Zou, Li, 2022. "Linear projections of joint symmetry and independence applied to exact testing treatment effects based on multidimensional outcomes," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    8. Jiajuan Liang & Kai Wang Ng & Guoliang Tian, 2019. "A class of uniform tests for goodness-of-fit of the multivariate $$L_p$$ L p -norm spherical distributions and the $$l_p$$ l p -norm symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 137-162, February.
    9. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    10. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.
    11. Schott, James R., 2003. "Kronecker product permutation matrices and their application to moment matrices of the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 177-190, October.
    12. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    13. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    14. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    15. Liebscher Eckhard & Richter Wolf-Dieter, 2020. "Modelling with star-shaped distributions," Dependence Modeling, De Gruyter, vol. 8(1), pages 45-69, January.
    16. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    17. Ricardo Fraiman & Leonardo Moreno & Sebastian Vallejo, 2017. "Some hypothesis tests based on random projection," Computational Statistics, Springer, vol. 32(3), pages 1165-1189, September.
    18. Dimitrios Thomakos & Johannes Klepsch & Dimitris N. Politis, 2020. "Model Free Inference on Multivariate Time Series with Conditional Correlations," Stats, MDPI, vol. 3(4), pages 1-26, November.
    19. Liang, Jiajuan & Pan, William S.Y. & Yang, Zhen-Hai, 2004. "Characterization-based Q-Q plots for testing multinormality," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 183-190, December.
    20. Ali Genç, 2013. "Moments of truncated normal/independent distributions," Statistical Papers, Springer, vol. 54(3), pages 741-764, August.

    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:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01316-w. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.