A Robustness Property of James-Stein Estimate with Applications

Abstract

In this article, we propose a tilting formula in importance resampling, to reduce the amount of resampling necessary for the construction of bootstrap confidence regions for multivariate parameters: do not resample (in the bootstrap procedure) uniformly from the sample, but modify this distribution in order to get variance reduction. We also provide a general account of the importance resampling, in which it is related to the large deviation tilting. Efficiency of this alternative distribution are shown, together with numerical evidence.