General bootstrap for dual phi-divergence estimates

TL;DR

This paper introduces a general bootstrap method for dual phi-divergence estimators, analyzing their asymptotic properties, practical implementation issues, and demonstrating their finite sample performance through simulations.

Contribution

It develops a unified bootstrap framework for dual phi-divergence estimates, including asymptotic analysis and practical guidance for implementation.

Findings

Asymptotic properties are established using empirical process theory.

Bootstrap confidence sets achieve correct coverage asymptotically.

Simulation results show good finite sample performance of the estimators.

Abstract

A general notion of bootstrapped $\phi$-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrapped $\phi$-divergence estimates are obtained, by mean of the empirical process theory, which are applied to construct the bootstrap confidence set with asymptotically correct coverage probability. Some of practical problems are discussed, including in particular, the choice of escort parameter and several examples of divergences are investigated. Simulation results are provided to illustrate the finite sample performance of the proposed estimators.