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Approximating a class of goodness-of-fit test statistics

Author

Listed:
  • Alba Fernández, M.V.
  • Jiménez Gamero, M.D.
  • Castillo Gutiérrez, S.

Abstract

A class of goodness-of-fit tests is considered. The test statistic of each test in this class is an L2-norm of the difference between the empirical characteristic function associated with a random sample and an estimator of the characteristic function of the population in the null hypothesis. Because it is not always possible to give an easily computable analytic expression of the test statistic, a numerical integration formula is given to approximate it. The approximation is built by considering a piecewise quadratic Taylor expansion. The null distribution of the resultant test statistic is consistently estimated by means of a bootstrap estimator. A simulation study is carried out to illustrate the accuracy of the numerical approximation, the goodness of the bootstrap estimator of the null distribution and the power of the test. Applications to real data sets are also provided.

Suggested Citation

  • Alba Fernández, M.V. & Jiménez Gamero, M.D. & Castillo Gutiérrez, S., 2014. "Approximating a class of goodness-of-fit test statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 24-38.
    • Handle: RePEc:eee:matcom:v:102:y:2014:i:c:p:24-38
    DOI: 10.1016/j.matcom.2013.04.025
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    References listed on IDEAS

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    1. V. Alba Fernández & D. Barrera Rosillo & M. Ibáñez Pérez & M. Jiménez Gamero, 2009. "A homogeneity test for bivariate random variables," Computational Statistics, Springer, vol. 24(3), pages 513-531, August.
    2. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    3. Muneya Matsui & Akimichi Takemura, 2008. "Goodness-of-fit tests for symmetric stable distributions—Empirical characteristic function approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 546-566, November.
    4. Nadarajah, Saralees & Gupta, Arjun K., 2007. "A generalized gamma distribution with application to drought data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 1-7.
    5. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
    6. Nora Gürtler & Norbert Henze, 2000. "Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 267-286, June.
    7. Muneya Matsui & Akimichi Takemura, 2005. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 183-199, March.
    8. M. V. Alba & D. Barrera & M. D. Jiménez, 2001. "A homogeneity test based on empirical characteristic functions," Computational Statistics, Springer, vol. 16(2), pages 255-270, July.
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    Cited by:

    1. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2015. "An approximation to the null distribution of a class of Cramér–von Mises statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 258-272.

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