Dual divergence estimators and tests: robustness results

TL;DR

This paper investigates the robustness and efficiency of dual phi-divergence estimators and tests in statistical models, proposing new hypothesis tests and evaluating their performance through simulations under various data conditions.

Contribution

It introduces and analyzes the robustness properties of dual phi-divergence estimators and tests, including new hypothesis testing procedures with empirical performance evaluation.

Findings

Estimators exhibit robustness to data contamination.

Proposed tests maintain good performance under contamination.

Simulation results support theoretical robustness claims.

Abstract

The class of dual $\phi$-divergence estimators (introduced in Broniatowski and Keziou (2009) is explored with respect to robustness through the influence function approach. For scale and location models, this class is investigated in terms of robustness and asymptotic relative efficiency. Some hypothesis tests based on dual divergence criterions are proposed and their robustness properties are studied. The empirical performances of these estimators and tests are illustrated by Monte Carlo simulation for both noncontaminated and contaminated data.