Comparison of the Methodology for Hypothesis Testing of the Independence of Two-Dimensional Random Variables Based on a Nonparametric Classifier

Abstract—

The properties of a new method for the hypothesis testing of the independence of random variables based on the use of a nonparametric pattern recognition algorithm corresponding to the maximum likelihood criterion are considered. The estimation of the distribution laws in classes is carried out using the initial statistical data under the assumption of the independence and dependence of the analyzed random variables. Under these conditions, estimates of the probabilities of pattern recognition errors in classes are calculated. A decision is made on the independence or dependence of random variables according to their minimum value. The results of the proposed method are compared using the Pearson criterion and the Pearson, Spearman, and Kendall correlation coefficients. When implementing the Pearson criterion, the formula for optimal discretization of the range of values of a two-dimensional random variable is used. Their effectiveness in complicating the dependence between random variables and changing the volume of initial statistical data is studied using computational experiment.