Technique for fast selection of blur coefficients of kernel functions of nonparametric regression

Abstract

To increase the computational efficiency of nonparametric regression, a method has been developed for fast selecting the blur coefficients of the kernel functions of nonparametric regression when restoring unambiguous stochastic dependencies. The application of the technique allows to significantly reduce the time spent in the synthesis of nonparametric regression in comparison with the traditional approach. The basis of the proposed methodology is the procedure for estimating the optimal blur coefficients of kernel functions for nonparametric estimation of the joint probability density of a family of dependent random variables with normal distribution laws. The method of selection the blur coefficients of nonparametric estimates of two dimensional probability density and regression of dependent random variables is investigated. The regularities of the influence of parameters of distributions of random variables and errors of their estimation on the efficiency indicators of the developed methodology are established. It is shown that the advantage of the proposed technique over the traditional approach is especially significant at small and large noise levels of the values of the function being restored.