The distribution of the maximal difference between a Brownian bridge and its concave majorant
Balabdaoui, Fadoua; Pitman, Jim (2011), The distribution of the maximal difference between a Brownian bridge and its concave majorant, Bernoulli, 17, 1, p. 466-483. http://dx.doi.org/10.3150/10-BEJ280
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0910.0405
Bernoulli Society for Mathematical Statistics and Probability
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Abstract (EN)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.
Subjects / KeywordsBrownian bridge; Brownian excursion; concave majorant; Doob’s transformation; inverse of Laplace transform; stick-breaking process
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Balabdaoui, Fadoua; Jankowski, Hanna; Rufibach, Kaspar; Pavlides, Marios (2013) Article accepté pour publication ou publié