半参数变系数部分线性模型的统计推断

Statistical inferences for semiparametric varying coefficient partially linear models

本文在多种复杂数据下,研究一类半参数变系数部分线性模型的统计推断理论和方法.首先在纵向数据和测量误差数据等复杂数据下,研究半参数变系数部分线性模型的经验似然推断问题,分别提出分组的和纠偏的经验似然方法.该方法可以有效地处理纵向数据的组内相关性给构造经验似然比函数所带来的困难.其次在测量误差数据和缺失数据等复杂数据下,研究模型的变量选择问题,分别提出一个"纠偏"的和基于借补值的变量选择方法.该变量选择方法可以同时选择参数分量及非参数分量中的重要变量,并且变量选择与回归系数的估计同时进行.通过选择适当的惩罚参数,证明该变量选择方法可以相合地识别出真实模型,并且所得的正则估计具有oracle性质.

In this paper, we mainly consider the inferences for a class of semiparametric varying coefficient par- tially linear models with complicated data. Firstly, we focus the empirical likelihood inferences for semiparametric varying coefficient partially linear models with complicated data, such as longitudinal data and data with measure- ment errors. A groupwise empirical likelihood method and a corrected empirical likelihood method are proposed, which can handle the inter-series dependence of the longitudinal data. Secondly, we consider the variable selection for semiparametric varying coefficient partially linear models with with complicated data, such as the data with measurement errors and missing data. A bias-corrected variable selection procedure and an imputation-based variable selection procedure are proposed. The proposed method can select significant variables in the parametric components and the nonparametric components simultaneously, and can simultaneously estimate regression coef- ficients in this variable selection procedure. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the regularized estimators are established.