New Statistical Kernel-Projection Estimator in the Monte Carlo Method

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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.

Original languageEnglish
Pages (from-to)313-317
Number of pages5
JournalDoklady Mathematics
Issue number1
Publication statusPublished - 1 Jul 2020


  • kernel density estimator
  • kernel-projection estimator
  • Monte Carlo method
  • projection estimator

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