统计与决策2025，Vol.41Issue(14)：47-52,6.DOI:10.13546/j.cnki.tjyjc.2025.14.008
基于核密度的线性惩罚样条光滑方法
A Linear Penalized Spline Smoothing Approach Based on Kernel Density
摘要
Abstract
The penalized spline smoothing method is a non-parametric statistical method used for data fitting and smoothing.It introduces penalty constraints in the spline function fitting process to reduce noise and irregularities.To achieve the best smoothing effect,choosing the best penalty term,penalty parameter and spline node remains a critical concern.In order to address these issues,this paper proposes a novel penalized spline smoothing approach based on ridge regression and kernel density tech-niques.The new approach uses kernel density at the spline nodes to construct the penalty matrix,and employs the ridge regression criterion as the penalty term for the spline coefficients.In addition,the approach employs a stepwise forward method for optimal spline node selection,and utilizes a matrix decomposition-based generalized cross-validation(GCV)criterion for fast and efficient penalty parameter selection,which significantly improves the computational speed.Simulation experiments demonstrate that the new method exhibits good fitting and prediction performance in various complex regression models.Notably,the proposed method exhibits strong predictive power over other regression methods in cases involving discontinuous regression models and explanatory variables with skewed distributions.关键词
ReLU/线性惩罚样条/非参数回归/节点选择/核密度/光滑方法Key words
ReLU/linear penalized spline/non-parametric regression/node selection/kernel density/smoothing method分类
数理科学引用本文复制引用
刘雨,晏梅..基于核密度的线性惩罚样条光滑方法[J].统计与决策,2025,41(14):47-52,6.基金项目
云南省科技厅科技计划青年项目(202201AU070051) （202201AU070051）
四川师范大学引进人才科研启动项目(rc20250216) （rc20250216）
云南师范大学博士科研启动项目(2020ZB014) （2020ZB014）
云南省现代应用数学与生命科学交叉融合创新团队(202405AS350003) （202405AS350003）
