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Application of the Family of Atomic Functions to Problems of a Nonparametric Probability Density Estimation


V. F. Kravchenko, V. I. Pustovoit, D. V. Churikov

In the given work for the first time on the basis of family of atomic functions (AF) nonparametric probability density estimations and its derivatives are considered. New designs of weight functions (WF) with the compact support are offered and proved. They allowing to build admissible estimations, both the probability density function and its derivatives 1st and 2nd orders. The urgency of application of nonparametric estimations in physical applications is caused by simplicity of structures and possibility of their use when the restored value is unknown. Therefore the new mathematical apparatus of nonparametric statistics received by means of the AF theory, will allow to estimate characteristics of investigated sequences without having the aprioristic parametrical information. The numerical experiment and the physical analysis of its results confirm efficiency of nonparametric characteristics estimation of stochastic process. Presence of parameters allows to expand applicability of the offered estimations to stochastic processes of the various physical nature. At increase of WF order we receive more smooth of probability density function estimation and at decrease more exact calculation of a mathematical expectation.

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