  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.
