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New Statistical Kernel-Projection Estimator in the Monte Carlo Method

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Abstract

The statistical kernel estimator in the Monte Carlo method is usually optimized based on the preliminary construction of a “microgrouped” sample of values of the variable under study. Even for the two-dimensional case, such optimization is very difficult. Accordingly, we propose a combined (kernel-projection) statistical estimator of the two-dimensional distribution density: a kernel estimator is constructed for the first (main) variable, and a projection estimator, for the second variable. In this case, for each kernel interval determined by the microgrouped sample, the coefficients of a particular orthogonal decomposition of the conditional probability density are statistically estimated based on preliminary results for the “micro intervals.” An important result of this work is the mean-square optimization of such an estimator under assumptions made about the convergence rate of the orthogonal decomposition in use. The constructed estimator is verified by evaluating the bidirectional distribution of a radiation flux passing through a layer of scattering and absorbing substance.

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ACKNOWLEDGMENTS

The computations were carried out using resources of the Shared Facility Center at the Siberian Supercomputer Center of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Science [10].

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00356.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    G. A. Mikhailov, N. V. Tracheva & S. A. Ukhinov

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    G. A. Mikhailov, N. V. Tracheva & S. A. Ukhinov

Authors
  1. G. A. Mikhailov
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  2. N. V. Tracheva
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  3. S. A. Ukhinov
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Corresponding authors

Correspondence to G. A. Mikhailov or N. V. Tracheva.

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Translated by I. Ruzanova

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Mikhailov, G.A., Tracheva, N.V. & Ukhinov, S.A. New Statistical Kernel-Projection Estimator in the Monte Carlo Method. Dokl. Math. 102, 313–317 (2020). https://doi.org/10.1134/S1064562420040122

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  • DOI: https://doi.org/10.1134/S1064562420040122

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