Testing the Hypothesis of the Independence of Two-Dimensional Random Variables Using a Nonparametric Algorithm for Pattern Recognition
Aleksandr V. Lapko, Vasiliy A. Lapko · Optoelectronics Instrumentation and Data Processing · 2021
Abstract A new method for testing the hypothesis of the independence of two-dimensional random variables is proposed. The method under consideration is based on the use of a nonparametric algorithm for pattern recognition that meets the maximum likelihood criterion. In contrast to the traditional problem statement, there is no training sample a priori. The initial information is represented by statistical data that make up the values of two-dimensional random variables. The laws of distribution of random variables in classes are estimated from the initial statistical data for the conditions of their dependence and independence. When choosing the optimal blur coefficients for nonparametric estimates of probability densities, the maximum of the likelihood functions is used as a criterion. Under these conditions, estimates of the probability of pattern recognition errors in classes are calculated. Based on the minimum value of the estimate of the probability of an error in pattern recognition, a decision is made on the independence or dependence of random variables. The effectiveness of the developed method is confirmed by the results of computational experiments when testing the hypothesis of the independence or linear dependence of two-dimensional random variables.