The distribution of the maximal difference between Brownian bridge and its concave majorant

Details The distribution of the maximal difference between Brownian bridge and its concave majorant The distribution of the maximal difference between Brownian bridge and its concave majorant

2009-10-02

arxiv.org/abs/0910.0405v1

Mathematics

Statistics Theory

18 pages, 3 figures

Scientific paper

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.

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