Abstract

A modification of the fast algorithm for the bandwidth selection of kernel functions in a nonparametric probability density estimate of the Rosenblatt–Parzen type is proposed. Fast algorithms for optimizing kernel estimates of probability densities make it possible to significantly reduce the calculation time when selecting their smoothing parameters (bandwidths) in comparison with the traditional approach, which is especially important when processing large statistical data. The method is based on the analysis of the formula for the optimal calculation of the smoothing parameter of kernel functions and the discovered dependence between the nonlinear functional on the second derivative of the reconstructed probability density and the antikurtosis coefficient. The proposed algorithm for the bandwidth selection provides a decrease in the probability density approximation error in comparison with the traditional approach. The findings are confirmed by the results of computational experiments. Special attention is paid to the dependence of these properties on the amount of initial data.

中文翻译：

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核密度估计带宽选择的改进快速算法

摘要

提出了一种对Rosenblatt–Parzen类型的非参数概率密度估计中的核函数带宽选择快速算法的改进。与传统方法相比，用于优化概率密度的内核估计的快速算法可以显着减少选择平滑参数（带宽）时的计算时间，这在处理大型统计数据时尤其重要。该方法基于对用于优化核函数平滑参数的公式的分析以及所发现的非线性函数对重构概率密度的二阶导数与抗峰度系数之间的依赖关系的分析。与传统方法相比，所提出的用于带宽选择的算法减少了概率密度近似误差。计算结果证实了这一发现。要特别注意这些属性对初始数据量的依赖性。