A moderate deviation principle for empirical bootstrap measure

Abstract

We prove two Large deviations principles (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measures given empirical probability measures. Second we establish LDP for the joint distributions of empirical measure and bootstrap empirical measures. Using these LDPs, similar LDPs for statistical differentiable functionals can be established. The LDPs for moderate deviations of empirical quantile processes and empirical bootstrap copula function are provided as illustration of these results.