Robert Keener

Much of my early research concerns the sequential design of experiments. My thesis seeks optimal designs in a simple versus simple setting, and led to my 1984 paper that gives near optimal designs in a rather general setting with a finite parameter space. Using mathematical ideas from my thesis, I later wrote two papers giving exact solutions to some bandit problems with arms governed by dichotomous parameters. My paper with Lerche and Woodroofe on optimal stopping may also be considered an aspect of sequential design. I remain interested in sequential design and several students have written dissertations in this area under my direction.

Much of the rest of my research concerns sequential analysis and related topics in probability theory. To a large extent asymptotic analysis is a unifying theme in this work. Two of my papers concern asymptotic expansions in multivariate renewal theory, three other papers concern asymptotic expansions for boundary crossing problems with nonlinear renewal theory scaling, and two other papers concern fluctuation theory. Most recently I have been interested in expansions to improve Brownian motion approximations. Finally, I have a number of collaborative papers in other areas of statistics.