k-Sample test based on the common area of kernel density estimators

In this paper we introduce a new k-sample test based on a certain distance among the kernel density estimators pertaining to the populations being compared. The considered distance (here denoted by AC) measures the area under the kernel estimators which is common to all of them, and the proposed test rejects the null hypothesis of equal distributions for small values of AC. The AC distance can be regarded as a generalization of the L1-norm to the k-sample problem. A simulation study (involving eight different test statistics) for k=3 suggests that the new test may be more powerful than previous tests, provided that the amount of smoothing is properly chosen. A Crámer-Chernoff type theorem is included, and the Bahadur slope of the proposed test statistic is derived.