The limit process of the difference between the empirical distribution function and its concave majorant
Vladimir N. Kulikov and Hendrik P. Lopuhaa
(2004) Technical Report. EURANDOM, the Netherlands.

## Abstract

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

EPrint Type: Monograph (Technical Report) Project Keyword UNSPECIFIED Learning/Statistics & Optimisation 787 Vladimir Koulikov 30 December 2004