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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (3): 306-314    
    
基于径向基的自适应惩罚样条回归模型
丁梦珍, 杨联强, 江坤, 王学军
安徽大学 数学科学学院, 安徽合肥 230601
Adaptive penalized spline regression model via radial basis
DING Meng-zhen, YANG Lian-qiang, JIANG Kun, WANG Xue-jun
School of Math. Sci., Anhui Univ., Hefei 230601, China
 全文: PDF 
摘要： 传统惩罚样条回归模型中惩罚项的设置未考虑数据的空间异质性, 因而对复杂数据的拟合缺乏自适应性. 文章通过对径向基函数的几何意义分析, 以节点两侧相邻区域内数据点的纵向极差为基础, 构造局部惩罚权重向量并加入到约束回归模型的惩罚项中, 构造了基于径向基的自适应惩罚样条回归模型. 新模型在观测数据波动较大的区域, 给予拟合曲线较小的惩罚, 而在观测数据波动较小的区域, 给予拟合曲线较大的惩罚, 从而使拟合曲线能自适应地反映观测数据的局部变化特征. 模拟和应用结果显示新模型的拟合效果显著优于传统的惩罚样条回归模型.
关键词： 非参回归;  惩罚样条;  自适应;  极差    
Abstract: Classical penalized regression model is inadequate of adaptivity for fitting complex data because that the spatial heterogeneity of observation data is not considered by the penalized term. According to the geometric meaning of radial basis, the local penalization vector based on the ranges of the data around each knot is constructed and added into the penalized term of the model. This new adaptive penalized spline regression model via radial basis gives less penalization to fitted curve where the observation data is volatile and more penalization to fitted curve where the observation data is flat, which makes the model adaptive to the local characterization of the sample points. Simulations and application show the fitting effect based on new model outperforms classical penalized spline regression model.
Key words: nonparametric regression    penalized spline    adaptivity    range
收稿日期: 2016-12-27 出版日期: 2018-04-07
:  O212.7  
基金资助: 国家自然科学基金(11671012); 安徽省自然科学基金(1708085MF163); 安徽省高校自然科学基金(KJ2017A028; KJ2017A024); 安徽大学数学科学学院开放课题(Y01002431)
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丁梦珍
杨联强
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王学军

引用本文:

丁梦珍, 杨联强, 江坤, 王学军. 基于径向基的自适应惩罚样条回归模型[J]. 高校应用数学学报, 2017, 32(3): 306-314.

DING Meng-zhen, YANG Lian-qiang, JIANG Kun, WANG Xue-jun. Adaptive penalized spline regression model via radial basis. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 306-314.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I3/306

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