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

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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.

This talk is part of the Statistics series.

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