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

Vladimir N. Kulikov and Hendrik P. Lopuhaä

Statistics & Probability Letters, 2006, vol. 76, issue 16, 1781-1786

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.

Keywords: Least; concave; majorant; Empirical; distribution; function; Brownian; motion; with; parabolic; drift; Isotonic; estimation; Monotone; density (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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