Hypothesis testing for two discrete populations based on the Hellinger distance

Our interest is in the problem where independent samples are drawn from two different discrete populations, possibly with a common parameter. The goal is to test hypothesis about the parameters involved in these two samples. A number of tests are developed for the above purpose based on the Hellinger distance and penalized versions of it. The asymptotic distributions of the test statistics are derived. Extensive simulation results are provided, which illustrate the theory developed and the robustness of the methods.