单指标模型自适应局部惩罚样条估计  

Adaptive Local Penalty Spline Estimation for Single Index Model

作　　者：赵静 ZHAO Jing(School of Statistics,Tianjin University of Finance and Economics,Tianjin 300202,China)

机构地区：[1]天津财经大学统计学院,天津300202

出　　处：《统计与信息论坛》2021年第4期3-11,共9页Journal of Statistics and Information

摘　　要：在单指标模型惩罚样条估计中,均匀惩罚样条由于各节点惩罚权重一致,导致在拟合过程中缺乏自适应性。为解决该问题,构建了一种基于变异系数的单指标模型自适应局部惩罚样条估计方法,利用径向基的局部惩罚样条逼近技术及Levenberg-Marquardt算法对模型的参数进行估计。首先,通过计算各节点中相邻区间数据的变异系数,构造局部惩罚权重矩阵,以变异系数的数值大小作为数据离散程度的判断标准。在数据离散程度大的区间,会给予拟合曲线较小的惩罚;在数据离散程度小的区间,会给予拟合曲线较大的惩罚,从而实现对样条系数的局部自适应调节,得到样条系数估计值。其次,使用“去一分量”法以及Levenberg-Marquardt算法得到单指标参数估计值。模拟仿真结果表明:基于变异系数的局部惩罚样条估计方法比均匀惩罚样条估计方法具有更好的拟合效果。在对比实验中可以看出,基于变异系数的局部惩罚样条估计方法拟合效果也略优于基于极差和方差的局部惩罚样条估计方法。In the penalty spline estimation of single index model,the uniform penalty spline is lack of self adaptability in the fitting process because the penalty weights of each node are consistent.In order to solve this problem,an adaptive local penalty spline estimation method based on coefficient of variation single index model is proposed in this paper.The local penalty spline approximation technique of radial basis function and Levenberg-Marquardt algorithm are used to estimate the parameters of the model.Firstly,the local penalty weight matrix is constructed by calculating the variation coefficient of the adjacent interval data in each node,and the value of the variation coefficient is used as the judgment standard of the degree of data dispersion.In the interval with large degree of data dispersion,the fitting curve will be given a smaller penalty;in the interval with small degree of data dispersion,the fitting curve will be given a larger penalty,so as to realize the optimization of the spline system Secondly,the“one component elimination”method and Levenberg-Marquardt algorithm are used to get the single index parameter estimation.The simulation results show that the local penalty spline estimation method based on variation coefficient has better fitting effect than the uniform penalty spline estimation method,and the fitting effect of the local penalty spline estimation method based on variation coefficient is slightly better than the local penalty spline estimation method based on range and variance.

关 键 词：单指标模型 局部惩罚样条估计 LEVENBERG-MARQUARDT算法 变异系数 

分 类 号：O212[理学—概率论与数理统计]