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Statistical inference for $$L^2$$ L 2 -distances to uniformity

Author

Listed:
  • L. Baringhaus

    (Leibniz Universität Hannover)

  • D. Gaigall

    (Leibniz Universität Hannover)

  • J. P. Thiele

    (Leibniz Universität Hannover)

Abstract

The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for $$L^2$$ L 2 -distances to uniformity based on the empirical distribution function, the integrated empirical distribution function and the integrated empirical survival function. Approximations of power functions, confidence intervals for the $$L^2$$ L 2 -distances and statistical neighbourhood-of-uniformity validation tests are obtained as main applications. The finite sample behaviour of the procedures is illustrated by a simulation study.

Suggested Citation

  • L. Baringhaus & D. Gaigall & J. P. Thiele, 2018. "Statistical inference for $$L^2$$ L 2 -distances to uniformity," Computational Statistics, Springer, vol. 33(4), pages 1863-1896, December.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:4:d:10.1007_s00180-018-0820-0
    DOI: 10.1007/s00180-018-0820-0
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    References listed on IDEAS

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    1. L. Baringhaus & N. Henze, 2017. "Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 167-188, April.
    2. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    3. Bernhard Klar, 2001. "Goodness-Of-Fit Tests for the Exponential and the Normal Distribution Based on the Integrated Distribution Function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 338-353, June.
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