The distribution of the maximal difference between Brownian bridge and its concave majorant
Statistics Theory
2009-10-05 v1 Statistics Theory
Abstract
We provide a representation of the maximal difference between a standard Brownian bridge and its concave majorant on the unit interval, from which we deduce expressions for the distribution and density functions and moments of this difference. This maximal difference has an application in nonparametric statistics where it arises in testing monotonicity of a density or regression curve.
Keywords
Cite
@article{arxiv.0910.0405,
title = {The distribution of the maximal difference between Brownian bridge and its concave majorant},
author = {Fadoua Balabdaoui and Jim Pitman},
journal= {arXiv preprint arXiv:0910.0405},
year = {2009}
}
Comments
18 pages, 3 figures