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Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies

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  • Bojana Milošević
  • Marko Obradović

Abstract

In this paper, new two-dimensional goodness-of-fit tests are proposed. They are of supremum type and are based on two different types of characterisations. The first type are those that involve functional equations that the distribution function satisfies, while the second type uses independence of some statistics. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process, a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:413-427
    DOI: 10.1080/10485252.2016.1163358
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    References listed on IDEAS

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    1. Jovanović, Milan & Milošević, Bojana & Nikitin, Ya. Yu. & Obradović, Marko & Volkova, K. Yu., 2015. "Tests of exponentiality based on Arnold–Villasenor characterization and their efficiencies," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 100-113.
    2. Alessandra Durio & Yacov Yu. Nikitin, 2001. "Local asympotic efficiency of some goodness-of-fit tests under skew alternatives," ICER Working Papers 04-2001, ICER - International Centre for Economic Research.
    3. Christophe Ley & Davy Paindaveine, 2009. "Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 943-967.
    4. Ya. Nikitin, 2010. "Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 649-668.
    5. 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.
    6. Ibrahim A. Ahmad & Ibrahim A. Alwasel, 1999. "A Goodness‐of‐fit Test for Exponentiality Based on the Memoryless Property," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 681-689.
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