半变系数纵向数据模型的渐近惩罚估计  

Penalized Asymptotic Estimation for Semi-variable Coefficient Models With Longitudinal Data

作　　者：赵明涛[1] Zhao Mingtao(School of Statistics and Applied Mathematics,Anhui University of Finance&Economics,Bengbu Anhui 233030,China)

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233030

出　　处：《统计与决策》2020年第13期34-38,共5页Statistics & Decision

基　　金：国家社会科学基金青年项目(15CTJ008)。

摘　　要：半变系数模型是线性模型和变系数模型的一种推广,该模型可以克服维数灾祸并具有较好的解释性。文章结合纵向数据研究半变系数模型的估计问题。首先利用多项式回归样条方法近似变系数,然后构造回归系数和样条系数的惩罚改进二次推断函数,进而得到模型的估计结果。最后建立估计过程的大样本性质,通过割线法得到估计结果在有限样本情况下的数值解。理论和数值结果显示,该方法具有良好的实用价值。The semi-variable coefficient model is a generalization of the linear model and the variable coefficient model,and it can overcome the curse of dimensionality and the lack of interpretability. This paper combines with longitudinal data to study the estimation of semi-variable coefficient models. Firstly, the paper uses the polynomial regression splines method to approximate the variable coefficients, and then constructs the penalized improved quadratic inference functions of regression coefficient and splines coefficients, with the estimation result obtained. Finally,The large sample property of the estimation process is established,and the numerical solutions of the estimation in the finite sample are obtained by secant method. Theoretical and numerical results show that the proposed method has good application value.

关 键 词：纵向数据 半变系数模型 割线法 

分 类 号：O212[理学—概率论与数理统计]