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On an independence test approach to the goodness-of-fit problem

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  • Baringhaus, Ludwig
  • Gaigall, Daniel

Abstract

Let X1,…,Xn be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R2→R and g:R2→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X1,X2),g(X1,X2) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xi,Xj),g(Xi,Xj)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.

Suggested Citation

  • Baringhaus, Ludwig & Gaigall, Daniel, 2015. "On an independence test approach to the goodness-of-fit problem," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 193-208.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:193-208
    DOI: 10.1016/j.jmva.2015.05.013
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    References listed on IDEAS

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    Cited by:

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    2. James S. Allison & Steffen Betsch & Bruno Ebner & Jaco Visagie, 2022. "On Testing the Adequacy of the Inverse Gaussian Distribution," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    3. Bojana Milošević & Marko Obradović, 2016. "Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 413-427, June.

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