A Fast Optimization Technique for the Regression Estimation of Probability Density of a One-Dimensional Random Variable

A method is proposed for the fast selection of the blurriness coefficient of kernel functions of the regression estimation of probability density of a one-dimensional random variable. Regression estimation of probability density is used in the analysis of large-volume statistical data. Its synthesis is based on compression of the initial information using sampling procedures of the range of values of a random variable and the formation of an array of transformed data. The elements of the resulting data array are the centers of sampling intervals and the corresponding frequencies of random variables from the initial sample. For a fast selection of the blurriness coefficient of kernel functions, the results of studying the asymptotic properties of the regression estimation of probability density are used. A method for estimating the components of the optimal blurriness coefficient is proposed. The method of computational experiment is used to analyze the effectiveness of the proposed approach for fast selection the blurriness coefficient of the regression estimation of probability density for a family of lognormal distribution laws for different volumes of initial data and promising procedures for sampling the range of values of a random variable.