COMPARISON OF THE METHODOLOGY FOR HYPOTHESIS TESTING OF THE INDEPENDENCE OF RANDOM VARIABLES BASED ON A NONPARAMETRIC CLASSIFIER AND THE PEARSON CRITERION
A. V. Lapko1,2, V. A. Lapko1,2, A.V. Bakhtina2
1Institute of Computational Modelling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, Russia
2Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia
Keywords: hypothesis testing of the independence of random variables, two-dimensional random variables, nonparametric pattern recognition algorithm, kernel probability density estimation, Pearson criterion, ambiguous functional dependencies
Abstract
The method of hypothesis testing of the independence of random variables, based on a nonparametric pattern recognition algorithm, is used in the analysis of ambiguous dependencies. The pattern recognition algorithm meets the maximum likelihood criterion. The estimation of the distribution laws in classes is carried out according to the initial statistical data under the assumption of independence and dependence of the compared random variables. Nonparametric statistics of the Rosenblatt - Parzen type are used to estimate probability densities in classes. The blur coefficients of kernel functions in nonparametric estimates of probability densities in classes are determined from the condition of the minimum of mean square deviations. Under these conditions, estimates of the probabilities of pattern recognition errors in classes are calculated. According to their minimum value, a decision is made on the independence or dependence of random variables. The hypothesis of a significant difference in the probabilities of pattern recognition errors in classes is tested. The application of the proposed technique allows us to bypass the problem of decomposition of the range of values of random variables into intervals, which is typical for the Pearson criterion. The effectiveness of the proposed method is compared with the Pearson criterion. The results of computational experiments using the studied criteria in the analysis of ambiguous dependencies between random variables are presented.
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