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Fast tests for the two-sample problem based on the empirical characteristic function

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  • Jiménez-Gamero, M.D.
  • Alba-Fernández, M.V.
  • Jodrá, P.
  • Barranco-Chamorro, I.

Abstract

A class of tests for the two-sample problem whose test statistic is an L2 norm of the difference of the empirical characteristic functions of the samples is considered. The null distribution can be estimated by means of bootstrap or permutation procedures. Although very easy to implement, such procedures can become computationally expensive as the sample size or the dimension of the data increase. This paper proposes to approximate the null distribution through a weighted bootstrap. The method is studied both theoretically and numerically. It provides a consistent estimator of the null distribution. The asymptotic properties are similar to those of the bootstrap and permutation estimators but, from a computational point of view, the weighted bootstrap estimator is more efficient. The proposed approach is also applied to the two-sample location problem and to the k-sample problem.

Suggested Citation

  • Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2017. "Fast tests for the two-sample problem based on the empirical characteristic function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 390-410.
    • Handle: RePEc:eee:matcom:v:137:y:2017:i:c:p:390-410
    DOI: 10.1016/j.matcom.2016.09.007
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    References listed on IDEAS

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    1. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
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    6. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    7. Ghoudi, Kilani & Rémillard, Bruno, 2014. "Comparison of specification tests for GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 291-300.
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    Cited by:

    1. 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).
    2. 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.
    3. 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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