Dual divergence estimators and tests: robustness results

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.