作　　者： ; ; ; ;

机构地区： 北京工业大学应用数理学院

出　　处： 《应用数学学报》 2007年第3期540-554,共15页

摘　　要： 纵向数据是数理统计研究中的复杂数据类型之一0,在生物、医学和经济学中具有广泛的应用．在实际中经常需要对纵向数据进行统计分析和建模．文章讨论了纵向数据下的半参数变系数部分线性回归模型,这里的纵向数据的在纵向观察在时间上可以是不均等的,也可看成是按某一随机过程来发生．所研究的半参数变系数模型包括了许多半参数模型,比如部分线性模型和变系数模型等．利用计数过程理论和局部线性回归方法,对于纵向数据下半参数变系数进行了统计推断,给出了参数分量和非参数分量的profile最小二乘估计,研究了这些估计的渐近性质,获得这些估计的相合性和渐近正态性． It is necessary to model and analyze longitudinal data in statistics, that are common complicated data in biostatistics, medicine and economics. Linear varying coefficient models are very important and useful in order to reduce the curse of dimensionality in statistical inferences. In this paper, we study semiparametric varying-coefficient partially linear model for general longitudinal data with different observing times, that is, the observation times may be irregular and be possibly considered as realizations from an arbitrary counting process. The proposal model may includes many useful semiparamtric models, such as partially linear models, varying-coefficient models. The profile least-squares estimators for the parametric component and nonparametric component are proposed by local linear regression technique. The asymptotic properties of the proposed estimators are studied. Consistency and asymptotic normality of the proposal estimators are established.

关 键 词： 变系数部分线性模型 局部线性回归 最小二乘 纵向数据 半参数模型

领　　域： [理学] [理学]