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

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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.

Original languageEnglish
Pages (from-to)341-353
Number of pages13
JournalRussian Journal of Numerical Analysis and Mathematical Modelling
Issue number6
Publication statusPublished - 1 Dec 2020


  • kernel statistical estimator
  • kernel-projective estimator
  • Monte Carlo method
  • orthogonal expansion
  • projective estimator
  • radiation transfer

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