Kernel Pattern Recognition Algorithm in the Task of Testing the Hypothesis of Distribution of Multidimensional Random Quantities

New method of testing hypotheses on distribution of multi-dimensional statistical data of large volume is considered. The possibility of replacing the hypothesis test on the identity of two laws of multivariate random values distribution with the hypothesis test on the equality of pattern recognition error with value 0,5 is proved. To test this hypothesis, the technique of trustworthy assessment of pattern recognition error probability or Kolmogorov-Smirnov test is used. Training sample is generated by statistical data of the compared distribution laws. Under conditions of large volumes of statistical data synthesis of nonparametric algorithm of pattern recognition is carried out on the basis of regression estimates of probability densities of random values distribution in classes. Proposed algorithms of pattern recognition allow reducing the amount of training sample due to decomposition of the range of random quantities values. Method of selection of decomposition optimal parameters of independent random values range is considered. The closest analogue of the proposed approach is the Pearson's chi-squared test.