IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-310014.html
   My bibliography  Save this paper

Fully Distribution-free Center-outward Rank Tests for Multiple-output Regression and Manova

Author

Listed:
  • Marc Hallin
  • Daniel Hlubinka
  • Sarka Hudecova

Abstract

Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks, hence carry all the “distribution-free information" available in the sample. We derive here the Hájek representation and asymptotic normality results required in the construction of center-outward rank tests for multiple-output regression and MANOVA. When based on appropriate spherical scores, these fully distribution-free tests achieve parametric efficiency in the corresponding models.

Suggested Citation

  • Marc Hallin & Daniel Hlubinka & Sarka Hudecova, 2020. "Fully Distribution-free Center-outward Rank Tests for Multiple-output Regression and Manova," Working Papers ECARES 2020-32, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/310014
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/310014/3/2020-32-HALLIN_HLUBINKA_HUDECOVA-fully.pdf
    File Function: Full text for the whole work, or for a work part
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    3. de Valk, Cees Fouad & Segers, Johan, 2018. "Stability and tail limits of transport-based quantile contours," LIDAM Discussion Papers ISBA 2018031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Beirlant, J. & Buitendag, S. & del Barrio, E. & Hallin, M. & Kamper, F., 2020. "Center-outward quantiles and the measurement of multivariate risk," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 79-100.
    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. Marc Hallin & Hongjian Shi & Mathias Drton & Fang Han, 2021. "Center-Outward Sign- and Rank-Based Quadrant, Spearman, and Kendall Tests for Multivariate Independence," Working Papers ECARES 2021-27, ULB -- Universite Libre de Bruxelles.
    2. del Barrio, Eustasio & González-Sanz, Alberto & Hallin, Marc, 2020. "A note on the regularity of optimal-transport-based center-outward distribution and quantile functions," Journal of Multivariate Analysis, Elsevier, vol. 180(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. Marc Hallin & Daniel Hlubinka & Šárka Hudecová, 2023. "Efficient Fully Distribution-Free Center-Outward Rank Tests for Multiple-Output Regression and MANOVA," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1923-1939, July.
    2. Hongjian Shi & Marc Hallin & Mathias Drton & Fang Han, 2020. "Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs," Working Papers ECARES 2020-23, ULB -- Universite Libre de Bruxelles.
    3. Beirlant, J. & Buitendag, S. & del Barrio, E. & Hallin, M. & Kamper, F., 2020. "Center-outward quantiles and the measurement of multivariate risk," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 79-100.
    4. Marc Hallin, 2021. "Measure Transportation and Statistical Decision Theory," Working Papers ECARES 2021-04, ULB -- Universite Libre de Bruxelles.
    5. María Edo & Walter Sosa Escudero & Marcela Svarc, 2021. "A multidimensional approach to measuring the middle class," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(1), pages 139-162, March.
    6. M. Hallin & D. La Vecchia & H. Liu, 2022. "Center-Outward R-Estimation for Semiparametric VARMA Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 925-938, April.
    7. Faugeras, Olivier P. & Rüschendorf, Ludger, 2021. "Functional, randomized and smoothed multivariate quantile regions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    8. Hongjian Shi & Mathias Drton & Marc Hallin & Fang Han, 2023. "Semiparametrically Efficient Tests of Multivariate Independence Using Center-Outward Quadrant, Spearman, and Kendall Statistics," Working Papers ECARES 2023-03, ULB -- Universite Libre de Bruxelles.
    9. Marc Hallin & Gilles Mordant, 2021. "On the Finite-Sample Performance of Measure Transportation-Based Multivariate Rank Tests," Working Papers ECARES 2021-24, ULB -- Universite Libre de Bruxelles.
    10. Alfred Galichon & Bernard Salani'e, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Papers 2106.02371, arXiv.org, revised Jan 2023.
    11. Davy Paindaveine & Germain Van Bever, 2017. "Halfspace Depths for Scatter, Concentration and Shape Matrices," Working Papers ECARES ECARES 2017-19, ULB -- Universite Libre de Bruxelles.
    12. Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    13. Gunsilius, Florian F., 2023. "A condition for the identification of multivariate models with binary instruments," Journal of Econometrics, Elsevier, vol. 235(1), pages 220-238.
    14. Petra Laketa & Stanislav Nagy, 2022. "Halfspace depth for general measures: the ray basis theorem and its consequences," Statistical Papers, Springer, vol. 63(3), pages 849-883, June.
    15. Marc Hallin & Hongjian Shi & Mathias Drton & Fang Han, 2021. "Center-Outward Sign- and Rank-Based Quadrant, Spearman, and Kendall Tests for Multivariate Independence," Working Papers ECARES 2021-27, ULB -- Universite Libre de Bruxelles.
    16. Alberto González-Sanz & Marc Hallin & Bodhisattva Sen, 2023. "Monotone Measure-Preserving Maps in Hilbert Spaces: Existence, Uniqueness, and Stability," Working Papers ECARES 2023-10, ULB -- Universite Libre de Bruxelles.
    17. Manuel Arellano & Stéphane Bonhomme, 2023. "Recovering Latent Variables by Matching," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 693-706, January.
    18. Florian Gunsilius & Susanne M. Schennach, 2019. "Independent nonlinear component analysis," CeMMAP working papers CWP46/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.
    20. Hudecová, Šárka & Šiman, Miroslav, 2022. "Multivariate ranks based on randomized lift-interdirections," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).

    More about this item

    Keywords

    Multivariate ranks; Multivariate signs; Multiple output regression; MANOVA; MANOVA; Rank test; Hájek representation;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:eca:wpaper:2013/310014. 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: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/arulbbe.html .

    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.