This article describes a methodology of and algorithmic means of testing the hypothesis of homogeneity of two distribution laws of multidimensional random variables using a pattern recognition algorithm that is based on kernel estimates of probability densities. The introduced classes are characterized according to the domain of the definition of the probability densities under consideration. On this basis, a training sample is formed from the initial statistical data and a pattern recognition algorithm is synthesized that corresponds to the maximum likelihood criterion using kernel estimates of probability densities. The original task of testing the hypothesis is replaced by testing the hypothesis that the pattern recognition error is equal to one half, which is possible when the analyzed distribution laws are close.
Lapko et al. (Sun,) studied this question.