A Technique for Rapid Selection of Blur Coefficients for Kernel Functions in Nonparametric Regression

A technique for rapid selection of blur coefficients for kernel functions in nonparametric regression is proposed. This technique increases the computational efficiency of nonparametric regression when reconstructing univariate stochastic dependencies. This technique can significantly reduce the time input required for the synthesis of nonparametric regression compared to the conventional approach. The proposed method is based on a procedure for estimating optimal blur coefficients of kernel functions for nonparametric estimation of the joint probability density of a family of dependent random variables that obey normal distribution. The possibility of a rapid selection of blur coefficients of nonparametric estimates of two-dimensional probability density and dependent random variable regression is investigated. The influence of random variable distribution parameters and their estimation errors on the efficiency of the developed methodology is established. The advantage of the proposed technique over the conventional approach is shown to be particularly significant at small and large noise levels of the values of the reconstructed function.