Longitudinal Data Part Of The Punishment Of The Linear Model Of Generalized Method Of Moments,

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.