TESTING OF A HYPOTHESIS ON INDEPENDENCE OF TWO-DIMENSIONAL RANDOM VALUES USING A NONPARAMETRIC ALGORITHM FOR PATTERN RECOGNITION
A. V. Lapko1,2, V. A. Lapko1,2
1Institute of Computational Modelling SB RAS, Krasnoyarsk, Russia
2Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia
Keywords: testing the hypothesis on independence of random variables, two-dimensional random variables, pattern recognition, kernel probability density estimation, maximum likelihood criterion, confidence estimation of probabilities
Abstract
A new method is proposed for testing a hypothesis on independence of two-dimensional random variables. The method under consideration is based on the use of a nonparametric pattern recognition algorithm 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, which are the values of two-dimensional random variables. The distribution laws of random variables in classes are estimated according to the initial statistical data for the conditions of their dependence and independence. In choosing the bandwidths for nonparametric probability density estimation, the maximum of the likelihood functions is used as a criterion. Under these conditions, the estimates of the probability of an error in pattern recognition in classes are calculated. Based on the minimum value of the estimate of the pattern recognition error probability, a decision is made whether the random variables are dependent or independent. The effectiveness of the developed technique is confirmed by the results of computational experiments with testing the hypothesis on independence or linear dependence of two-dimensional random variables.
|
