IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v67y2015i5p917-941.html
   My bibliography  Save this article

Depth-based runs tests for bivariate central symmetry

Author

Listed:
  • Rainer Dyckerhoff
  • Christophe Ley
  • Davy Paindaveine

Abstract

McWilliams (J Am Stat Assoc 85:1130–1133, 1990 ) introduced a nonparametric procedure based on runs for the problem of testing univariate symmetry about the origin (equivalently, about an arbitrary specified center). His procedure first reorders the observations according to their absolute values, then rejects the null when the number of runs in the resulting series of signs is too small. This test is universally consistent and enjoys good robustness properties, but is unfortunately limited to the univariate setup. In this paper, we extend McWilliams’ procedure into tests of bivariate central symmetry. The proposed tests first reorder the observations according to their statistical depth in a symmetrized version of the sample, then reject the null when an original concept of simplicial runs is too small. Our tests are affine invariant and have good robustness properties. In particular, they do not require any finite moment assumption. We derive their limiting null distribution, which establishes their asymptotic distribution freeness. We study their finite-sample properties through Monte Carlo experiments and conclude with some final comments. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:5:p:917-941
    DOI: 10.1007/s10463-014-0480-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-014-0480-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-014-0480-y?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. Davy Paindaveine & Germain Van bever, 2013. "From Depth to Local Depth: A Focus on Centrality," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1105-1119, September.
    2. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    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. 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.
    5. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    6. Modarres, Reza & Gastwirth, Joseph L., 1996. "A modified runs test for symmetry," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 107-112, December.
    7. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    8. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    9. 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. 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.
    2. 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.
    3. Ricardo Fraiman & Leonardo Moreno & Sebastian Vallejo, 2017. "Some hypothesis tests based on random projection," Computational Statistics, Springer, vol. 32(3), pages 1165-1189, September.
    4. Van Bever, Germain, 2016. "Simplicial bivariate tests for randomness," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 20-25.
    5. Ludwig Baringhaus & Norbert Henze, 2016. "Revisiting the two-sample runs test," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 432-448, September.
    6. Morgunov, V.I. (Моргунов, В.И.), 2016. "The Liquidity Management of the Banking Sector and the Short-Term Money Market Interest Rates [Управление Ликвидностью Банковского Сектора И Краткосрочной Процентной Ставкой Денежного Рынка]," Working Papers 21311, Russian Presidential Academy of National Economy and Public Administration.
    7. 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.
    8. Ivanović, Blagoje & Milošević, Bojana & Obradović, Marko, 2020. "Comparison of symmetry tests against some skew-symmetric alternatives in i.i.d. and non-i.i.d. setting," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).

    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. Rainer Dyckerhoff & Christophe Ley & Davy Paindaveine, 2014. "Depth-Based Runs Tests for bivariate Central Symmetry," Working Papers ECARES ECARES 2014-03, ULB -- Universite Libre de Bruxelles.
    2. Ricardo Fraiman & Leonardo Moreno & Sebastian Vallejo, 2017. "Some hypothesis tests based on random projection," Computational Statistics, Springer, vol. 32(3), pages 1165-1189, September.
    3. 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.
    4. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    5. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    6. M. D. Jiménez-Gamero & J. L. Moreno-Rebollo & J. A. Mayor-Gallego, 2018. "On the estimation of the characteristic function in finite populations with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 95-121, March.
    7. 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.
    8. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    10. Angelica Gianfreda & Derek Bunn, 2018. "A Stochastic Latent Moment Model for Electricity Price Formation," BEMPS - Bozen Economics & Management Paper Series BEMPS46, Faculty of Economics and Management at the Free University of Bozen.
    11. 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.
    12. Dai, Xinjie & Niu, Cuizhen & Guo, Xu, 2018. "Testing for central symmetry and inference of the unknown center," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 15-31.
    13. 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.
    14. repec:hal:spmain:info:hdl:2441/3qnaslliat80pbqa8t90240unj is not listed on IDEAS
    15. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    16. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    17. Sangyeol Lee & Simos G. Meintanis & Minyoung Jo, 2019. "Inferential procedures based on the integrated empirical characteristic function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 357-386, September.
    18. Neuhaus, Georg & Zhu, Li-Xing, 1998. "Permutation Tests for Reflected Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 129-153, November.
    19. Koltchinskii, V. I. & Li, Lang, 1998. "Testing for Spherical Symmetry of a Multivariate Distribution," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 228-244, May.
    20. James S. Allison & Charl Pretorius, 2017. "A Monte Carlo evaluation of the performance of two new tests for symmetry," Computational Statistics, Springer, vol. 32(4), pages 1323-1338, December.
    21. O‐Chia Chuang & Xiaojun Song & Abderrahim Taamouti, 2022. "Testing for Asymmetric Comovements," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1153-1180, October.

    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:aistmt:v:67:y:2015:i:5:p:917-941. 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.