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Affine invariant depth-based tests for the multivariate one-sample location problem

Author

Listed:
  • Sakineh Dehghan

    (University of Shahid Beheshti)

  • Mohammad Reza Faridrohani

    (University of Shahid Beheshti)

Abstract

A multivariate affine invariant family of depth-based tests is proposed for the one-sample location problem. Suitable outlyingness functions which are formulated using depth functions are used to construct the proposed tests. The asymptotic null distribution and the asymptotic relative efficiency of the tests are discussed under the class of centrally and elliptically symmetric distributions, respectively. Furthermore, a conditional distribution-free property of the tests is shown. The performance of the proposed tests is evaluated using a Monte Carlo study as well as asymptotic relative efficiencies and is compared to that of several competitors. It is observed that such tests yield a better performance as compared to their competitors for a wide spectrum of alternatives.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:3:d:10.1007_s11749-018-0593-3
    DOI: 10.1007/s11749-018-0593-3
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    References listed on IDEAS

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    1. Möttönen, J. & Hettmansperger, T. P. & Oja, H. & Tienari, J., 1998. "On the Efficiency of Affine Invariant Multivariate Rank Tests," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 118-132, July.
    2. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
    3. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    4. Yijun Zuo, 2009. "Data Depth Trimming Counterpart of the Classical (or ) Procedure," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-9, December.
    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. Rousson, Valentin, 2002. "On Distribution-Free Tests for the Multivariate Two-Sample Location-Scale Model," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 43-57, January.
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    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. Dehghan, Sakineh & Faridrohani, Mohammad Reza, 2024. "A data depth based nonparametric test of independence between two random vectors," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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