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Estimation of a nonlinear functional from the probability density when optimizing nonparametric decision functions
https://doi.org/10.32446/0368-1025it.2021-1-14-20
Abstract
A method for estimating the nonlinear functional of the probability density of a two-dimensional random variable is proposed. It is relevant when implementing procedures for fast bandwidths selection in the problem of optimization of kernel probability density estimates. The solution of this problem allows to signifi cantly improve the computational efficiency of nonparametric decision rules. The basis of the proposed approach is the analysis of the formula for the optimal bandwidth of the kernel probability density estimation. In this case, the bandwidth of kernel functions is represented as the product of an indeterminate parameter and the average square deviations of random variables. The main component of an undefined parameter is a nonlinear functional of the probability density. The considered functional is determined by the type of probability density and does not depend on the density parameters. For a family of two-dimensional lognormal laws of distribution of independent random variables, the approximation errors of the considered nonlinear functional from the probability density are determined. The possibility of applying the proposed methodology when evaluating nonlinear functionals of probability densities that differ from the lognormal distribution laws is investigated. An analysis is made of the effect of the resulting approximation errors on the root-mean-square criteria for restoring a non-parametric estimate of the probability density of a two-dimensional random variable.
About the Authors
A. V. Lapko
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences (ICM SB RAS);
Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Aleksandr V. Lapko
Krasnoyarsk
V. A. Lapko
Institute of Computational Modeling, Siberian Branch of the Russian Academy of Sciences (ICM SB RAS);
Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Vasiliy A. Lapko
Krasnoyarsk
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Review
For citations:
Lapko A.V., Lapko V.A. Estimation of a nonlinear functional from the probability density when optimizing nonparametric decision functions. Izmeritel`naya Tekhnika. 2021;(1):14-20. (In Russ.) https://doi.org/10.32446/0368-1025it.2021-1-14-20
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