IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v188y2022ics0167715222000979.html
   My bibliography  Save this article

Asymptotic efficiency of some nonparametric tests for location on hyperspheres

Author

Listed:
  • Dabo-Niang, Sophie
  • Thiam, Baba
  • Verdebout, Thomas

Abstract

In the present paper, we show that several classical nonparametric tests for multivariate location in the Euclidean case can be adapted to nonparametric tests for the location problem on hyperspheres. The tests we consider are spatial signed-rank tests for location on hyperspheres. We compute the asymptotic powers of the latter tests in the classical rotationally symmetric case. In particular, we show that the spatial signed-rank test uniformly dominates the spatial sign test and has performances that are extremely close to the asymptotically optimal test in the well-known von Mises–Fisher case. Monte-Carlo simulations confirm our asymptotic results.

Suggested Citation

  • Dabo-Niang, Sophie & Thiam, Baba & Verdebout, Thomas, 2022. "Asymptotic efficiency of some nonparametric tests for location on hyperspheres," Statistics & Probability Letters, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:stapro:v:188:y:2022:i:c:s0167715222000979
    DOI: 10.1016/j.spl.2022.109524
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222000979
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109524?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. T. Hayakawa, 1990. "On tests for the mean direction of the Langevin distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 359-373, June.
    2. Eduardo Garcia-Portugues & Davy Paindaveine & Thomas Verdebout, 2020. "On optimal tests for rotational symmetry against new classes of hyperspherical distributions," Post-Print hal-03169388, HAL.
    3. Ko, D. J. & Chang, T., 1993. "Robust M-Estimators on Spheres," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 104-136, April.
    4. Eduardo García-Portugués & Davy Paindaveine & Thomas Verdebout, 2020. "On Optimal Tests for Rotational Symmetry Against New Classes of Hyperspherical Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1873-1887, December.
    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. Janice L. Scealy, 2021. "Comments on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 68-70, March.
    2. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.
    3. Davy Paindaveine & Joséa Rasoafaraniaina & Thomas Verdebout, 2021. "Preliminary test estimation in uniformly locally asymptotically normal models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 689-707, June.
    4. Xu, Danli & Wang, Yong, 2023. "Density estimation for spherical data using nonparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    5. Kim, Byungwon & Schulz, Jörn & Jung, Sungkyu, 2020. "Kurtosis test of modality for rotationally symmetric distributions on hyperspheres," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    6. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    7. Luca Greco & Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection," Stats, MDPI, vol. 4(2), pages 1-18, June.
    8. Davy Paindaveine & Thomas Verdebout, 2019. "Inference for Spherical Location under High Concentration," Working Papers ECARES 2019-02, ULB -- Universite Libre de Bruxelles.
    9. Shogo Kato & Shinto Eguchi, 2016. "Robust estimation of location and concentration parameters for the von Mises–Fisher distribution," Statistical Papers, Springer, vol. 57(1), pages 205-234, March.
    10. Yoko Watamori, 1992. "Tests for a given linear structure of the mean direction of the langevin distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 147-156, March.
    11. Giovanni Saraceno & Claudio Agostinelli & Luca Greco, 2021. "Robust estimation for multivariate wrapped models," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 225-240, August.
    12. Arnab Kumar Laha & A. C. Pravida Raja & K. C. Mahesh, 2019. "SB-robust estimation of mean direction for some new circular distributions," Statistical Papers, Springer, vol. 60(3), pages 877-902, June.
    13. Kirschstein, Thomas & Liebscher, Steffen & Pandolfo, Giuseppe & Porzio, Giovanni C. & Ragozini, Giancarlo, 2019. "On finite-sample robustness of directional location estimators," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 53-75.
    14. Chang, Ted & Tsai, Ming-Tien, 2003. "Asymptotic relative Pitman efficiency in group models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 395-415, May.
    15. Bernard, Gaspard & Verdebout, Thomas, 2024. "On some multivariate sign tests for scatter matrix eigenvalues," Econometrics and Statistics, Elsevier, vol. 29(C), pages 252-260.

    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:stapro:v:188:y:2022:i:c:s0167715222000979. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.