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A Class of Goodness-of-fit Tests Based on Transformation

Author

Listed:
  • Simos G. Meintanis
  • Ma Dolores JimÉnez Gamero
  • V. Alba-fernÁndez

Abstract

There is an increasing number of goodness-of-fit tests whose test statistics measure deviations between the empirical characteristic function and an estimated characteristic function of the distribution in the null hypothesis. With the aim of overcoming certain computational difficulties with the calculation of some of these test statistics, a transformation of the data is considered. To apply such a transformation, the data are assumed to be continuous with arbitrary dimension, but we also provide a modification for discrete random vectors. Practical considerations leading to analytic formulas for the test statistics are studied, as well as theoretical properties such as the asymptotic null distribution, validity of the corresponding bootstrap approximation, and consistency of the test against fixed alternatives. Five applications are provided in order to illustrate the theory. These applications also include numerical comparison with other existing techniques for testing goodness-of-fit.

Suggested Citation

  • Simos G. Meintanis & Ma Dolores JimÉnez Gamero & V. Alba-fernÁndez, 2014. "A Class of Goodness-of-fit Tests Based on Transformation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(8), pages 1708-1735, April.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:8:p:1708-1735
    DOI: 10.1080/03610926.2012.673673
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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. 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. 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.

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