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Integral distribution-free statistics of Lp-type and their asymptotic comparison

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  • Henze, Norbert
  • Nikitin, Yakov
  • Ebner, Bruno

Abstract

Generalizing the Cramér-von Mises and the Kolmogorov-Smirnov test, different integral statistics based on Lp-norms are compared with respect to local approximate Bahadur efficiency. Simulation results corroborate the theoretical findings. Several examples illustrate that goodness-of-fit testing based on Lp-norms should receive more attention. It is shown that, given a distribution function F0 and a specific alternative, one can draw the plot of efficiency as a function of p and determine the value of p giving the maximum efficiency.

Suggested Citation

  • Henze, Norbert & Nikitin, Yakov & Ebner, Bruno, 2009. "Integral distribution-free statistics of Lp-type and their asymptotic comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3426-3438, July.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3426-3438
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    References listed on IDEAS

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    Cited by:

    1. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.
    2. Bojana Milošević & Marko Obradović, 2016. "New class of exponentiality tests based on U-empirical Laplace transform," Statistical Papers, Springer, vol. 57(4), pages 977-990, December.
    3. Majid Mojirsheibani & William Pouliot, 2017. "Weighted bootstrapped kernel density estimators in two-sample problems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 61-84, January.
    4. Mojirsheibani, Majid, 2012. "A weighted bootstrap approximation of the maximal deviation of kernel density estimates over general compact sets," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 230-241.

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