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Fast goodness-of-fit tests based on the characteristic function

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  • Jiménez-Gamero, M. Dolores
  • Kim, Hyoung-Moon

Abstract

A class of goodness-of-fit tests whose test statistic is an L2 norm of the difference of the empirical characteristic function of the sample and a parametric estimate of the characteristic function in the null hypothesis, is considered. The null distribution is usually estimated through a parametric bootstrap. Although very easy to implement, the parametric bootstrap can become very computationally expensive as the sample size, the number of parameters or the dimension of the data increase. It is proposed 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. In the numerical examples carried out, the estimated type I errors are close to the nominal values. The asymptotic properties are similar to those of the parametric bootstrap but, from a computational point of view, it is more efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:89:y:2015:i:c:p:172-191
    DOI: 10.1016/j.csda.2015.03.015
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    References listed on IDEAS

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    1. 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.
    2. Meintanis, S.G. & Milošević, B. & Jiménez–Gamero, M.D., 2024. "Goodness–of–fit tests based on the min–characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    3. Elizabeth González-Estrada & José A. Villaseñor & Rocío Acosta-Pech, 2022. "Shapiro-Wilk test for multivariate skew-normality," Computational Statistics, Springer, vol. 37(4), pages 1985-2001, September.
    4. M. D. Jiménez-Gamero & A. Batsidis, 2017. "Minimum distance estimators for count data based on the probability generating function with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 503-545, July.
    5. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2021. "A test for the geometric distribution based on linear regression of order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 103-123.
    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. Kim, SungBum & Kim, Hyoung-Moon, 2022. "Series form of the characteristic functions of scale mixtures of multivariate skew-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 172-187.

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