树结构变窗宽局部多项式拟合方法  

Tree Structure Variable Bandwidth Local Polynomial Fitting Method

作　　者：刘晓芳 王合玲[2] 张辉国[1] LIU Xiao-fang;WANG He-ling;ZHANG Hui-guo(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China;College of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830012,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046 [2]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012

出　　处：《数学的实践与认识》2023年第11期142-149,共8页Mathematics in Practice and Theory

基　　金：新疆自然科学基金(2019D01C045);教育部人文社会科学研究规划基金(19YJA910007);国家自然科学基金(11961065);国家社会科学基金(16BTJ024)。

摘　　要：变窗宽局部多项式模型是探索被估计曲线复杂变化结构的有力工具,其关键思想在于针对不同变化模式的数据区间选择不同窗宽参数进行拟合.基于回归树模型提出一种变窗宽多项式拟合方法,利用回归树的分类功能识别具有不同变化结构的数据区间,在每个子区间上独立选取最优窗宽,通过局部多项式回归实现复杂结构曲线的变窗宽拟合.随机模拟的结果表明,回归树能够有效识别具有不同变化模式的数据区间,变窗宽局部多项式拟合均方误差小,具有计算高效、结果易解释的特点.The variable bandwidth local polynomial model is a powerful data-driven tool for analyzing complex structures of the estimated curve.It is the key idea of the variable bandwidth smoothing methods that the variable bandwidths are chose to fit the estimated curve in the data sub-intervals with different varying patterns.This paper proposes a variable bandwidth polynomial fitting method based on a decision tree model.The decision tree is used to identify sub-intervals of data with different varying structures and the optimal bandwidth is independently selected in each sub-interval,and then the variable bandwidth local polynomial model is employed to fit the curve with complex structures.The results of the simulations show that the decision tree can effectively identify sub-intervals with different patterns,and the local polynomial fitting method with variable bandwidth has a small mean square error.The proposed method has various nice features of high calculation eficiency and easyinterpretability.

关 键 词：回归树 变窗宽 局部多项式 交叉验证 

分 类 号：O212.1[理学—概率论与数理统计]