Geodesic
New statistical kernel-projection estimator in the Monte Carlo method
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 62-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: kernel density estimator, projection estimator, kernel-projection estimator, Monte Carlo method. 
@article{DANMA_2020_493_a12,
     author = {G. A. Mikhailov and N. V. Tracheva and S. A. Uhinov},
     title = {New statistical kernel-projection estimator in the {Monte} {Carlo} method},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {62--67},
     year = {2020},
     volume = {493},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_493_a12/}
}
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G. A. Mikhailov; N. V. Tracheva; S. A. Uhinov. New statistical kernel-projection estimator in the Monte Carlo method. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 62-67. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a12/

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