Abstract 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.

中文翻译：

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蒙特卡罗方法中一种新的核投影统计估计器

摘要 在本文中，我们提出了一种新的二维分布密度组合核-射影统计估计量，其中第一个“主”变量用核估计量处理，第二个用射影估计量处理条件分布密度。在这种情况下，条件分布密度的一些正交扩展的统计估计系数用于由微样本定义的每个“内核”间隔。这种估计器的均方根优化是在关于所用正交展开的收敛速度的假设下进行的。对构造的估计器的数值研究是针对物质层前向散射和后向散射的辐射通量的角分布实施的。