78 citations · 336 across the 32 of their papers we have counts for
9 papers · 1 filter
Grenander functionals and Cauchy's formula
Piet Groeneboom
Let be the nonparametric maximum likelihood estimator of a decreasing density. Grenander characterized this as the left-continuous slope of the least concave majorant of…
Chernoff's distribution and differential equations of parabolic and Airy type
Piet Groeneboom, Steven Lalley, Nico Temme
We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argum…
The remaining area of the convex hull of a Poisson process
Piet Groeneboom
In Cabo and Groeneboom (1994) the remaining area of the left-lower convex hull of a Poisson point process with intensity one in the first quadrant of the plane was analyzed, using…
Convex hulls of uniform samples from a convex polygon
Piet Groeneboom
In Groeneboom (1988) a central limit theorem for the number of vertices of the convex hull of a uniform sample from the interior of convex polygon was derived. In the unpublished p…
The tail of the maximum of Brownian motion minus a parabola
Piet Groeneboom, Nico M. Temme
We analyze the tail behavior of the maximum N of Brownian motion minus a parabola and give an asymptotic expansion for P(N>x) as x tends to infinity. This extends a first order res…
Vertices of the least concave majorant of Brownian motion with parabolic drift
Piet Groeneboom
It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, whi…