In this talk we will propose several goodness-of-fit tests for the k-sample problem. Specifically, we will
focus on tests based on a distance among the kernel density estimators pertaining to the k populations
being compared. The performance of the proposed tests will be explored via simulations, in which (for comparison purposes)
some other traditional and recent tests for the k-sample problem will be considered too. Since the power of the
tests based on the kernel density estimates varies with the smoothing degree, optimal automatic bandwidth selection
will be discussed.