Analysis of signals, audio and video information

A fast optimization technique for the regression estimation of the probability density of a one-dimensional random variable

A. V. Lapko^ab, А. L. Vasily<sup>ab

a</sup> Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
^b M. F. Reshetnev Siberian State University of Science and Technologies, Krasnoyarsk, Russia

Abstract: A method is proposed for the fast selection of the blurriness coefficient of the kernel functions of the regression estimation of the probability density of a one-dimensional random variable. For a fast selection, the results of studying the asymptotic properties of the regression estimate of the 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 a fast selection of the blurriness coefficient of the regression estimate of the 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.

Keywords: regression estimation of probability density, large volume samples, selection of blurriness coefficients, sampling of the range of values of random variables, lognormal distribution law.

DOI: 10.14357/20718594240210

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