Non-parametric k-sample tests: Density functions vs distribution functions

In this paper we introduce some tests for the comparison of k samples based on kernel density estimators (KDE), and we develope the Double Minimum method as a new and useful procedure for the crucial problem of bandwidth selection. We study, via Monte Carlo simulations, the statistical power of the proposed tests, as well as the impact of the smoothing degree and the performance of the Double Minimum algorithm. Finally, we compare the results of the tests based on the KDE to those of the traditional k-sample tests based on empirical distribution functions (EDF), and to other tests based on the likelihood ratio introduced in the recent literature. Two main conclusions are obtained. First, the proposed bandwidth selection method attain quasi-optimal results. Second, the simulations suggest that KDE-based tests are the most powerful when the underlying populations are different in shape.