New test for the multivariate two-sample problem based on the concept of minimum energy

We introduce a new statistical quantity, the energy, to test whether two samples originate from the same distributions. The energy is a simple logarithmic function of the distances of the observations in the variate space. The distribution of the test statistic is determined by a resampling method. The power of the energy test in one dimension was studied for a variety of different test samples and compared to several nonparametric tests. In two and four dimensions, a comparison was performed with the Friedman-Rafsky and nearest neighbor tests. The two-sample energy test was shown to be especially powerful in multidimensional applications.