PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

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:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:787
Deposited By:Vladimir Koulikov
Deposited On:30 December 2004