TY - JOUR

T1 - A new kernel-projective statistical estimator in the Monte Carlo method

AU - Mikhailov, Gennady A.

AU - Tracheva, Natalya V.

AU - Ukhinov, Sergey A.

N1 - Publisher Copyright: © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In the present paper, we propose a new combined kernel-projective statistical estimator of the two-dimensional distribution density, where the first 'main' variable is processed with the kernel estimator, and the second one is processed with the projective estimator for the conditional distribution density. In this case, statistically estimated coefficients of some orthogonal expansion of the conditional distribution density are used for each 'kernel' interval defined by a micro-sample. The root-mean-square optimization of such an estimator is performed under the assumptions concerning the convergence rate of the used orthogonal expansion. The numerical study of the constructed estimator is implemented for angular distributions of the radiation flux forward-scattered and backscattered by a layer of matter. A comparative analysis of the results is performed for molecular and aerosol scattering.

AB - In the present paper, we propose a new combined kernel-projective statistical estimator of the two-dimensional distribution density, where the first 'main' variable is processed with the kernel estimator, and the second one is processed with the projective estimator for the conditional distribution density. In this case, statistically estimated coefficients of some orthogonal expansion of the conditional distribution density are used for each 'kernel' interval defined by a micro-sample. The root-mean-square optimization of such an estimator is performed under the assumptions concerning the convergence rate of the used orthogonal expansion. The numerical study of the constructed estimator is implemented for angular distributions of the radiation flux forward-scattered and backscattered by a layer of matter. A comparative analysis of the results is performed for molecular and aerosol scattering.

KW - kernel statistical estimator

KW - kernel-projective estimator

KW - Monte Carlo method

KW - orthogonal expansion

KW - projective estimator

KW - radiation transfer

UR - http://www.scopus.com/inward/record.url?scp=85098186020&partnerID=8YFLogxK

U2 - 10.1515/rnam-2020-0028

DO - 10.1515/rnam-2020-0028

M3 - Article

AN - SCOPUS:85098186020

VL - 35

SP - 341

EP - 353

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 6

ER -