Tests of hypotheses in discrete models based on the penalized Hellinger distance

Analogues of the likelihood ratio, Rao, and Wald tests are introduced in discrete parametric models based on the family of penalized Hellinger distances. It is shown that the tests based on a particular member of this family provide attractive alternatives to the tests based on the ordinary Hellinger distance. These tests share the robustness of the Hellinger distance test, but are often closer to the likelihood-based tests at the model, especially in small samples. The convergence of ordinary Hellinger distance tests to limiting [chi]2 distributions are quite slow. The proposed tests are improvements in this respect.