115 citations · 496 across the 33 of their papers we have counts for
5 papers · 1 filter
Distribution-free properties of isotonic regression
Jake A. Soloff, Adityanand Guntuboyina, Jim Pitman
It is well known that the isotonic least squares estimator is characterized as the derivative of the greatest convex minorant of a random walk. Provided the walk has exchangeable i…
Gaps and interleaving of point processes in sampling from a residual allocation model
Jim Pitman, Yuri Yakubovich
This article presents a limit theorem for the gaps between order statistics of a sample of size f…
Random weighted averages, partition structures and generalized arcsine laws
Jim Pitman
This article offers a simplified approach to the distribution theory of randomly weighted averages or -means , for a sequence of i.i.d.random variable…
Squared Bessel processes of positive and negative dimension embedded in Brownian local times
Jim Pitman, Matthias Winkel
The Ray--Knight theorems show that the local time processes of various path fragments derived from a one-dimensional Brownian motion are squared Bessel processes of dimensions…
A guide to Brownian motion and related stochastic processes
Jim Pitman, Marc Yor
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, mos…