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

Fadoua Balabdaoui (1) , Pitman Jim (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [Berkeley]

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.

Domaines: Théorie [stat.TH]

Fadoua Balabdaoui, Pitman Jim. The distribution of the maximal difference between a Brownian bridge and its concave majorant. Bernoulli, 2011, 17, pp.466--483. ⟨hal-00701838⟩