Nonparametric method for testing the hypothesis of independence of random variables and its application in the analysis of remote sensing data

Testing the hypothesis of independence of random variables is one of the main stages of system analysis of statistical data. Based on its results, a synthesis of effective decision-making algorithms is carried out. The traditional method of testing the hypothesis of independence of random variables is based on the use of the Pearson criterion, which contains a difficult to formalize stage of dividing the range of values of random variables into multidimensional intervals. A method for testing the hypothesis of independence of random variables is proposed, which uses a nonparametric pattern recognition algorithm corresponding to the maximum likelihood criterion. Its application makes it possible to circumvent the problem of decomposing the range of values of random variables into intervals. The idea of the approach is to form a training sample based on the initial statistical data to solve a two-alternative pattern recognition problem. Each class is defined under the assumption of independence or dependence of random variables, which is manifested in the difference in their distribution laws in the classes. Under these conditions, it becomes possible to replace the initial hypothesis with the task of checking the reliability of the difference in the probabilities of pattern recognition errors in classes. Using the apparatus of graph theory, the proposed method is developed in the formation of sets of independent random variables. The obtained results are generalized when testing the hypothesis of independence of random variables for large volumes of statistical data based on compression of the original information. This allows to increase the computational efficiency of the problem being solved. The article substantiates a method for testing the hypothesis of independence of random variables, based on the use of a nonparametric pattern recognition algorithm in conditions of large volumes of statistical data. The results of comparing the technique with the generally recognized Pearson consensus criterion in the study of ambiguous dependencies between random variables of varying complexity are presented. The effectiveness of the proposed method is confirmed by the results of its application in processing remote sensing information from anthropogenic territories in the vicinity of the city of Krasnoyarsk.