Large Deviation Principle for moderate deviation probabilities of empirical bootstrap measure

We prove two LDPs (LDP) in the zone of moderate deviation probabilities. First we establish LDP for the conditional distributions of moderate deviations of empirical bootstrap measure given empirical probability measure. Second we establish LDP for the joint distribution of empirical measure and empirical bootstrap measure. Using these LDPs, on the base of contraction principle, we deduce similar LDPs for statistical functionals having the Hadamard derivatives. The LDPs for moderate deviations of empirical quantile processes and empirical bootstrap copula function are given as illustration of these results.