Large deviations for bootstrapped empirical measures

Abstract

We investigate the Large Deviations (LD) properties of bootstrapped empirical measures with exchangeable weights. Our main results show in great generality how the resulting rate functions combine the LD properties of both the sample weights and the observations. As an application, we obtain new LD results and discuss both conditional and unconditional LD-efficiency for many classical choices of entries such as Efron’s, leave-$p$-out, i.i.d. weighted, $k$-blocks bootstraps, etc.