Formation of sets of independent components of a multidimensional random variable based on a nonparametric pattern recognition algorithm

Abstract

The possibility of circumventing the problem of decomposition of the range of values of random variables when testing various hypotheses is considered. A brief review of the literature on this problem is given. A method for forming sets of independent components of a multidimensional random variable is proposed, based on hypotheses testing about the independence of paired combinations of components of a multidimensional random variable. The method uses a two-dimensional non-parametric algorithm for pattern recognition of the kernel type, corresponding to the criterion of maximum likelihood. In contrast to the traditional method based on the application of the Pearson criterion, the proposed approach avoids the problem of decomposing the range of values of random variables into multidimensional intervals. The results of computational experiments performed according to the method of forming sets of independent random variables are presented. Using the information obtained, an information graph is constructed, the vertices of which correspond to the components of a multidimensional random variable, and the edges determine their independence. Then the vertices of the complete subgraphs correspond to groups of independent components of a random variable. The obtained results form the basis for the synthesis of a multi-level nonparametric large volume data processing system, each level of which corresponds to a specific set of independent random variables.