Statistics is concerned with making sense or inferences about the world based on limited information and uncertainties. In contrast, mathematics is exact. The goal is to prove theorems based on a well-defined set of assumptions. It is the juxtaposition of statistics and mathematics that I find intriguing and challenging. Mathematical statistics serves to precisely quantify and explain what can be learned through "experimentation," in spite of having to acknowledge our uncertainty in the process.
While my own research has been theoretically oriented, much of it has been motivated by a desire to understand practical statistical methodology to obtain techniques that may be applied safely in practice. I have been particularly interested in advancing "nonparametric" techniques that do not rely on the statistician having to invoke unverifiable assumptions. In my work, I have tried to explore the extent of applicability of bootstrap and resampling methods, as well as understanding their limitations. My recent interests have focused on extending resampling methods to problems in time series analysis.