Some new non-asymptotic results about the accuracy of the weighted bootstrap

Stochastics Seminar
Thursday, April 28, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 006
School of Mathematics, Georgia Tech
The bootstrap procedure is well known for its good finite-sample performance, though the majority of the present results about its accuracy are asymptotic. I will study the accuracy of the weighted (or multiplier) bootstrap procedure for estimation of quantiles of a likelihood ratio statistic. The set-up is the following: the sample size is bounded, random observations are independent, but not necessarily identically distributed, and a parametric model can be misspecified. This problem had been considered in the recent work of Spokoiny and Zhilova (2015) with non-optimal results. I will present a new approach improving the existing results.