We consider the possibility of circumventing the decomposition problem for the range of values of random variables when testing various hypotheses. A brief review of the literature on this issue is given. A method is proposed for forming sets of independent components of a multidimensional random variable, based on testing hypotheses about the independence of paired combinations of components of a multidimensional random variable. The method uses a two-dimensional nonparametric algorithm for the recognition of kernel-type patterns, corresponding to the criterion of maximum likelihood. In contrast to the traditional technique using Pearson’s criterion, the proposed technique avoids the problem of decomposing the range of values of random variables into multidimensional intervals. We present results of computational experiments performed using the method of forming sets of independent random variables. From the obtained data, an information graph is constructed, whose vertices correspond to the components of a multidimensional random variable, and the edges determine their independence, while the vertices of the complete subgraphs correspond to groups of independent components of the random variable. The results obtained form the basis for the synthesis of a multilevel nonparametric system for processing large volumes of data, each level of which corresponds to a specific set of independent random variables.