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New goodness-of-fit tests based on fiducial empirical distribution function

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  • Xu, Xingzhong
  • Ding, Xiaobo
  • Zhao, Shuran

Abstract

In this paper we derive new tests for goodness of fit based on the fiducial empirical distribution function (EDF) after the probability integral transformation of the sample. Note that the fiducial EDF for a set of given sample observations is a randomized distribution function. By substituting the fiducial EDF for the classical EDF in the Kolmogorov-Smirnov, Cramér-von Mises statistics and so forth, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. It emerges from Monte Carlo simulations that in most cases there exist some of the new tests having better power properties than the corresponding tests based on the classical EDF and Pyke's modified EDF.

Suggested Citation

  • Xu, Xingzhong & Ding, Xiaobo & Zhao, Shuran, 2009. "New goodness-of-fit tests based on fiducial empirical distribution function," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1132-1141, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1132-1141
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    References listed on IDEAS

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    1. Jin Zhang, 2002. "Powerful goodness‐of‐fit tests based on the likelihood ratio," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 281-294, May.
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    Cited by:

    1. Daojiang He & Xingzhong Xu, 2013. "A goodness-of-fit testing approach for normality based on the posterior predictive distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 1-18, March.
    2. T. Fischer & U. Kamps, 2013. "Power maps in goodness-of-fit testing," Computational Statistics, Springer, vol. 28(3), pages 1365-1382, June.

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