Comparison of Methods for Testing the Hypothesis of Independence of Random Variables Based on a Nonparametric Classifier and Pearson’s Chi-Squared Test
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引用次数: 0
Abstract
A technique for testing the hypothesis about 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 assessment of distribution laws in classes is carried out using initial statistical data under the assumption of independence and dependence of the random variables being compared. To estimate probability densities in classes, nonparametric Rosenblatt–Parzen statistics are used. The blurring coefficients of kernel functions in nonparametric estimates of probability densities in classes are determined from the condition of the minimum of their standard deviations. Under these conditions, estimates of the probabilities of pattern recognition errors in classes are calculated. Based on their minimum value, a decision is made on the independence or dependence of random variables. The hypothesis about a significant difference in the probabilities of pattern recognition errors in classes is tested. The use of the proposed technique allows us to bypass the problem of decomposing the range of values of random variables into intervals, which is characteristic of 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.
期刊介绍：
The scope of Optoelectronics, Instrumentation and Data Processing encompasses, but is not restricted to, the following areas: analysis and synthesis of signals and images; artificial intelligence methods; automated measurement systems; physicotechnical foundations of micro- and optoelectronics; optical information technologies; systems and components; modelling in physicotechnical research; laser physics applications; computer networks and data transmission systems. The journal publishes original papers, reviews, and short communications in order to provide the widest possible coverage of latest research and development in its chosen field.
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