纵向数据部分线性模型的惩罚广义矩方法

【作者】 倪艳风；

【导师】 朱仲义；

【作者基本信息】 复旦大学 ， 统计学， 2009， 硕士

【摘要】 纵向数据是指对每一个个体在不同的时间点进行观测而得到的由截面和时间序列融合在一起的数据,因此它既可以分析出个体随时间的变化趋势,又可以分析总体的变化趋势。对于半参数部分线性模型,通常的做法是用样条方法或者核方法逼近非参数部分,然后再用线性模型的估计方法去估计参数部分。参数部分的估计可以采用传统的广义线性模型方法(GLM)、广义估计方程方法(GEE)或者二次推断函数方法(QIF),然而,对于某些依赖于时间的协变量而言,上述的估计方法的效率是不足的。本文在引入Lai和Small(2007)对依赖于时间的协变量的分类基础上,使用p-样条拟合非参数函数,对不同的矩条件用不同的广义矩方法对模型的参数和非参数进行估计,并且给出了估计量的大样本性质;我们用计算机模拟和算例证明了当模型中存在不同的矩条件时,采用不同的惩罚广义矩方法可以显著地提高估计精度。更多还原

【Abstract】 Longitudinal data is referred to data in which individuals are measured repeatedly over time,so it combines elements of cross-sectional data and time-series data.It can not only analyze effectively the change of individuals over time, but also be of use in prediction of the population.In this paper,we focused on partial linear model,which is semi-parametrical.The general procedure is to make an approximation of the nonparametric part by kernel estimation or spline estimation in the first step,followed by the parametric estimation with traditional method,including Generalized Linear Model(GLM),Generalized Estimating Equation(GEE),or Quadratic Inference Function(QIF).However,with some specified covariates,these methods will result in a loss in efficiency.In this paper,on the basis of the classification of the time-dependent covariates given by Lain and Small(2007),we fit the nonparametric part with P-spline, and estimate the parametrical and nonparametric part with different Generalized method of moments estimation for different moment conditions,implemented by the proof of the asymptotical properties for the estimator,which is also been proved by simulation and illustrative example,from which we can also find out that different penalized general method of moments estimations for different moment conditions perform more efficiently.更多还原