Large deviations for bootstrapped empirical measures

TL;DR

This paper studies the large deviations behavior of bootstrapped empirical measures with exchangeable weights, revealing how their rate functions integrate properties of weights and observations, and deriving new large deviation principles.

Contribution

It provides a general framework for understanding large deviations of bootstrapped empirical measures, unifying existing results and establishing new principles.

Findings

Unified large deviation principles for bootstrapped measures

Recovery of known conditional and unconditional LDPs

Derivation of new large deviation results for bootstrap methods

Abstract

We investigate the Large Deviations properties of bootstrapped empirical measure with exchangeable weights. Our main result shows in great generality how the resulting rate function combines the LD properties of both the sample weights and the observations. As an application we recover known conditional and unconditional LDPs and obtain some new ones.