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Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant

Author

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  • Vladimir N. Kulikov

    (ING Financial Markets)

  • Hendrik P. Lopuhaä

    (Delft University of Technology)

Abstract

We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L k -type distances. In the case of a uniform distribution, we also establish their limit distribution together with that of the supremum distance. It turns out that in the uniform case, the measures of deviation are of greater order and their limit distributions are different.

Suggested Citation

  • Vladimir N. Kulikov & Hendrik P. Lopuhaä, 2008. "Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant," Journal of Theoretical Probability, Springer, vol. 21(2), pages 356-377, June.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:2:d:10.1007_s10959-007-0103-0
    DOI: 10.1007/s10959-007-0103-0
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    References listed on IDEAS

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    1. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    2. Wang, Yazhen, 1994. "The limit distribution of the concave majorant of an empirical distribution function," Statistics & Probability Letters, Elsevier, vol. 20(1), pages 81-84, May.
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    Cited by:

    1. Graham Elliott & Nikolay Kudrin & Kaspar Wuthrich, 2022. "The Power of Tests for Detecting $p$-Hacking," Papers 2205.07950, arXiv.org, revised Apr 2024.

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