函数型部分线性模型的参数估计及其变量选择  

Parameter estimation and variable selection for functional partially linear models

作　　者：袁晓惠 曹儒雅 金宛霖 YUAN Xiao-hui;CAO Ru-ya;JIN Wan-lin(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《吉林师范大学学报（自然科学版）》2022年第2期48-56,共9页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11901053,11671054);吉林省科技发展计划项目(20210101149JC)。

摘　　要：考虑了函数型部分线性模型,它既有函数型数据,又有标量型数据,是一个应用较为广泛的函数型回归模型.使用基于B样条的光滑技术与函数型光滑消边绝对偏离技术(fSCAD)相结合的方法给出了斜率函数的局部稀疏估计,并用SCAD方法给出了标量型系数的估计.通过模拟分析,显示了局部稀疏估计方法的有限样本表现.最后,通过一个实例来说明估计方法的优越性与实用性.A functional partial linear model,which had both functional data and scalar data,was a widely used functional regression model.In addition,the use of B-spline-based smoothing technology and functional smoothing edge elimination absolute deviation technology(fSCAD)combined method gave the local sparse estimation of the slope function,and uses the SCAD method was used to give the estimation of the scalar type coefficient.Through simulation analysis,the limited sample performance of the local sparse estimation method was shown.Finally,an example was used to illustrate the advantages and practicability of the estimation method.

关 键 词：函数型数据 B样条基函数 SCAD 最小二乘估计 光滑技术 

分 类 号：O212[理学—概率论与数理统计]