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The limit process of the difference between the empirical distribution function and its concave majorant

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  • Kulikov, Vladimir N.
  • Lopuhaä, Hendrik P.

Abstract

We consider the process -Fn, being the difference between the empirical distribution function Fn and its least concave majorant , corresponding to a sample from a decreasing density. We extend Wang's result on pointwise convergence of -Fn and prove that this difference converges as a process in distribution to the corresponding process for two-sided Brownian motion with parabolic drift.

Suggested Citation

  • Kulikov, Vladimir N. & Lopuhaä, Hendrik P., 2006. "The limit process of the difference between the empirical distribution function and its concave majorant," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1781-1786, October.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:16:p:1781-1786
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    References listed on IDEAS

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    1. 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. Lopuhaä, Hendrik P. & Musta, Eni, 2018. "The distance between a naive cumulative estimator and its least concave majorant," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 119-128.

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    2. Lopuhaä, Hendrik P. & Musta, Eni, 2018. "The distance between a naive cumulative estimator and its least concave majorant," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 119-128.

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