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math.ST2009
The distribution of the maximal difference between Brownian bridge and its concave majorant
Fadoua Balabdaoui, Jim Pitman
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 dis…
math.ST2007★ 12 cited
A Kiefer--Wolfowitz theorem for convex densities
Fadoua Balabdaoui, Jon A. Wellner
Kiefer and Wolfowitz [Z. Wahrsch. Verw. Gebiete 34 (1976) 73--85] showed that if is a strictly curved concave distribution function (corresponding to a strictly monotone densit…