纵向数据非参数模型的惩罚修正二次推断函数估计  

Penalized Modified Quadratic Inference Functions for Nonparametric Models with Longitudinal Data

作　　者：赵明涛[1,2] 何晓群[1] 

机构地区：[1]中国人民大学统计学院,北京100872 [2]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150001

出　　处：《数学的实践与认识》2013年第5期193-199,共7页Mathematics in Practice and Theory

摘　　要：基于纵向数据研究非参数模型y=f(t)+ε,其中f(·)为未知平滑函数,ε为零均值随机误差项.利用截断幂函数基对f(·)进行基函数展开近似,并且结合惩罚样条的方法构造关于基函数系数的惩罚修正二次推断函数.然后利用割线法迭代得到基函数系数估计的数值解,从而得到未知平滑函数的估计.理论证明,应用此方法所得到的基函数系数估计具有相合性和渐近正态性.最后通过数值方法得到了较好的拟合结果.In this paper, we study the nonparametric models y=f（t） ＋ε with longitudinal data, where f（·） is the unknown smooth function and ε is the zero-mean random term. We approximate the unknown smooth function f（·） by truncated power basis expansion and establish the penalized modified quadratic inference functions about coefficients of basis functions by the method of penalized splines. Then we get the numerical solution of coefficients of the basis functions using secant method and the estimator of the unknown smooth function. Theoretical result shows that the proposed method has consistency and asymptotic properties. Moreover, we also get good fitted results by numerical method.

关 键 词：纵向数据 非参数模型 惩罚修正二次推断函数 割线法 

分 类 号：O212.1[理学—概率论与数理统计]