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Tests for the multivariate -sample problem based on the empirical characteristic function

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  • Marie Hušková
  • Simos Meintanis

Abstract

Tests for the multivariate k-sample problem are considered. The tests are based on the weighted L2 distance between empirical characteristic functions, and afford an interesting interpretation in terms of a corresponding test statistic based on the L2 distance of pairs of non-parametric density estimators. Depending on the choice of weighting, a corresponding Dirac-type weight function reduces the test to a normalised version of the L2 distance between the sample means of the k populations. Theoretical and computational issues are considered, while the finite-sample implementation based on the permutation distribution of the test statistic shows that the new test performs well in comparison with alternative procedures of the change-point type.

Suggested Citation

  • Marie Hušková & Simos Meintanis, 2008. "Tests for the multivariate -sample problem based on the empirical characteristic function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 263-277.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:263-277
    DOI: 10.1080/10485250801948294
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    Cited by:

    1. L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.
    2. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    3. Cousido-Rocha, Marta & de Uña-Álvarez, Jacobo & Hart, Jeffrey D., 2019. "A two-sample test for the equality of univariate marginal distributions for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    4. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    5. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    6. G. I. Rivas-Martínez & M. D. Jiménez-Gamero & J. L. Moreno-Rebollo, 2019. "A two-sample test for the error distribution in nonparametric regression based on the characteristic function," Statistical Papers, Springer, vol. 60(4), pages 1369-1395, August.
    7. 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.
    8. M. Jiménez Gamero, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 412-413, September.
    9. Cécile Durot & Piet Groeneboom & Hendrik P. Lopuhaä, 2013. "Testing equality of functions under monotonicity constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 939-970, December.
    10. M. D. Jiménez-Gamero & M. Cousido-Rocha & M. V. Alba-Fernández & F. Jiménez-Jiménez, 2022. "Testing the equality of a large number of populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-21, March.
    11. 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.
    12. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    13. Fu, Zhonghao & Hong, Yongmiao & Wang, Xia, 2023. "Testing for structural changes in large dimensional factor models via discrete Fourier transform," Journal of Econometrics, Elsevier, vol. 233(1), pages 302-331.
    14. 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.
    15. Ansgar Steland, 2016. "Asymptotics for random functions moderated by dependent noise," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 363-387, October.
    16. 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.

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