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.

中文翻译：

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使用用于模式识别的非参数算法测试二维随机变量独立性的假设

摘要

提出了一种检验二维随机变量独立性假设的新方法。正在考虑的方法基于使用非参数算法进行模式识别，以满足最大似然标准。与传统的问题陈述相反，没有先验的训练样本。初始信息由构成二维随机变量值的统计数据表示。随机变量在类中的分布规律是根据它们的依赖和独立条件从初始统计数据中估计出来的。当为概率密度的非参数估计选择最佳模糊系数时，似然函数的最大值被用作标准。在这些条件下，计算类中模式识别错误概率的估计值。根据模式识别错误概率估计的最小值，对随机变量的独立性或相关性做出决定。在检验二维随机变量的独立性或线性相关性假设时，计算实验的结果证实了所开发方法的有效性。