Gilles Blanchard  (joint with E. Roquain and S. Arlot)

Title: Resampling-based confidence regions in high dimension from a non-asymptotic point of view


Abstract:

We study generalized bootstrapped confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure, with a non-asymptotic control of the confidence level. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution.

We consider two approaches, the first based on a concentration principle and the second on a direct boostrapped quantile. The first
one allows us to deal with a very large class of resampling weights while our results for the second are restricted to Rademacher weights. The non-asymtpotic point of view developed here is strongly inspired by recent work in the area of learning theory.