部分线性模型的高斯径向基函数估计
Gaussian Radial Basis Function Estimation of Partially Linear Model
DOI: 10.12677/ORF.2023.135528, PDF,   
作者: 胡怀青：贵州大学数学与统计学院，贵州 贵阳
关键词: 高斯径向基函数；部分线性模型；B样条；Gaussian Radial Basis Function； Partially Linear Models； B-Spline
摘要: 部分线性模型是一种常用的现代统计模型，其同时具备参数与非参数回归的优点。我们基于高斯径向基函数估计部分线性模型的非线性部分，并给出估计过程中的超参数选择方法。在模拟仿真与实证分析中将高斯径向基函数与B样条进行对比，发现高斯径向基函数在部分线性模型中可以成为B样条的一种替代方法。
Abstract: The partially linear model is a commonly used modern statistical model with the advantages of both parametric and nonparametric regression. We estimate the nonlinear part of the partially linear model based on the Gaussian radial basis function, and give the hyperparameter selection method in the estimation process. The Gaussian radial basis function is compared with the B-spline in simulation and empirical analysis, and it is found that the Gaussian radial basis function can be an alternative method to the B-spline in the partially linear model.
文章引用：胡怀青. 部分线性模型的高斯径向基函数估计[J]. 运筹与模糊学, 2023, 13(5): 5266-5274. https://doi.org/10.12677/ORF.2023.135528

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