倒向随机微分方程中非参数估计的核函数选择

Kernel Function Selection of Nonparametric Estimation of Backward Stochastic Differential Equation

比较了多种类型的核函数下倒向随机微分方程(BSDE)中生成元z的非参数估计方法,利用不同的核函数估计BSDE中的生成元z的非参数估计,在均方误差意义下比较了8种不同的核函数下得到的BSDE的生成元z的非参数估计的精度,统计分析结果显示Gaussian核函数下的估计效果最好。

The comparison of several kernel functions in nonparametric estimation of generator z of backward stochastic differential equation（BSDE） are discussed in this paper.Utilizing different kernel functions for nonparametric estimation of generator z of BSDE,the estimation accuracies of 8 kernel functions in terms of mean squares error（MSE） are investigated,the experimental results with statistical methods show that the estimation effectiveness of Gaussian kernel function is the best.