INVESTIGATION OF THE METHOD FOR TESTING THE HYPOTHESIS OF THE INDEPENDENCE OF TWO-DIMENSIONAL RANDOM VARIABLES USING A NONPARAMETRIC CLASSIFIER
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: testing the hypothesis of the independence of random variables, two-dimensional random variables, nonparametric pattern recognition algorithm, kernel probability density estimation, criterion of the maximum likelihood, Pearson's criterion, dependent random variables
Abstract
The properties of the method for testing the hypothesis of theindependence of random variables based on the use of a nonparametric pattern recognition algorithm corresponding to the maximum likelihood criterion are investigated. The distribution laws in the classes are estimated on the basis of the initial statistical data, assuming the independence and dependence of the compared random variables. Under these conditions, the estimates of the probability of an error in pattern recognition in classes are calculated. Based on their minimum value, a decision is made on the independence or dependence of random variables. The application of the proposed technique allows us to circumvent the problem of decomposition of the range of values of random variables into multidimensional intervals. The effectiveness of the proposed technique with the complication of the relationship between random variables and changes in the volume of the initial statistical data is investigated by the method of computational experiments.
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