Comparison of Methods for Testing the Hypothesis of Independence of Random Variables Based on a Nonparametric Classifier and Pearson’s Chi-Squared Test

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...

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Vydáno v:Optoelectronics, instrumentation, and data processing Ročník 59; číslo 5; s. 551 - 560
Hlavní autoři: Lapko, A. V., Lapko, V. A., Bakhtina, A. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.10.2023
Témata:
Analysis and Synthesis of Signals and Images
Lasers
Optical Devices
Optics
Photonics
Physics
Physics and Astronomy
ambiguous functional dependences
kernel probability density estimate
testing the hypothesis of independence of random variables
two-dimensional random variables
nonparametric pattern recognition algorithm
Pearson’s chi-squared test
ISSN:8756-6990, 1934-7944
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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.
AbstractList 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.
Author Lapko, A. V.
Bakhtina, A. V.
Lapko, V. A.
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Keywords ambiguous functional dependences
kernel probability density estimate
testing the hypothesis of independence of random variables
two-dimensional random variables
nonparametric pattern recognition algorithm
Pearson’s chi-squared test
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SubjectTerms Analysis and Synthesis of Signals and Images
Lasers
Optical Devices
Optics
Photonics
Physics
Physics and Astronomy
Title 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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