删失数据下的半参数变系数部分线性回归模型

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 71-85.

删失数据下的半参数变系数部分线性回归模型

罗羡华, 李元, 马昀蓓, 周勇

广州大学数学与信息科学学院广州510006

收稿日期:2007-11-30 修回日期:2009-02-09 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
罗和李的研究获得国家自然科学基金(10671044),广州市教育局项目(2004)和广州市科技局项目(2004J1-C0333)资助; 周和马的工作得到国家杰出青年基金项目(70825004), 国家杰出青年基金B项目(10721101)资助, 国家自然科学基金重点项目(10731010), 国家自然科学基金委创新研究群体科学基金(10721101),国家973项目子项目(2007CB814902)和国家自然科学基金委杰出青年基金B项目(10628104)资助. 并获得上海财经大学``十五''``211工程"重点学科建设项目和上海财经大学``211工程"期重点学科建设项目资助.

Varying-Coefficient Partially Linear Models with Censored Data

LUO Xian-Hua, LI Yuan, MA Yun-Bei, ZHOU Yong

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006

Received:2007-11-30 Revised:2009-02-09 Online:2010-01-01 Published:2010-01-01
Supported by:
罗和李的研究获得国家自然科学基金(10671044),广州市教育局项目(2004)和广州市科技局项目(2004J1-C0333)资助; 周和马的工作得到国家杰出青年基金项目(70825004), 国家杰出青年基金B项目(10721101)资助, 国家自然科学基金重点项目(10731010), 国家自然科学基金委创新研究群体科学基金(10721101),国家973项目子项目(2007CB814902)和国家自然科学基金委杰出青年基金B项目(10628104)资助. 并获得上海财经大学``十五''``211工程"重点学科建设项目和上海财经大学``211工程"期重点学科建设项目资助.

摘要/Abstract

摘要：

为了分析删失数据,该文考虑变系数部分线性模型, 此模型允许协变量对响应变量存在非线性影响. 响应变量与协变量之间关系的统计模型通过线性结构来拟合是非常重要而且有益. 对于删失数据, 常用的统计方法不能直接应用于此模型. 该文首先提出一类数据变换用以建立无偏条件期望.
然后利用profile最小二乘方法,给出了模型中参数分量和非参数分量的profile最小二乘估计, 并建立了这些估计的渐近正态性. 最后通过数值例子来说明该文所提出的方法的有效性.

关键词: 变系数部分线性模型, 局部线性回归, profile最小二乘, 删失, 变换

Abstract:

This paper considers varying-coefficient partially linear model, which allows one to examine the extent to which covariates interact
nonlinearly with an exposure variable, for analysis of censored data. It is very important and useful to fit statistical models by linear construction for response and covariates. For censored data, the usual statistical techniques are not directly applicable to this model. In this paper, we propose a class of transformations of the data so that a unbiased conditional expectation is established. Then the profile least-squares estimators for the parametric and nonparametric components are proposed by profile least-squares technique. The asymptotic normality of the proposed estimators are established. Some numerical examples are given to illustrate the effectiveness of the proposed procedures.

Key words: Varying-coefficient, Partially linear models, Local linear regression, Profile least squares, Censoring, Transformation

中图分类号:

62N05

罗羡华, 李元, 马昀蓓, 周勇. 删失数据下的半参数变系数部分线性回归模型[J]. 数学物理学报, 2010, 30(1): 71-85.

LUO Xian-Hua, LI Yuan, MA Yun-Bei, ZHOU Yong. Varying-Coefficient Partially Linear Models with Censored Data[J]. Acta mathematica scientia,Series A, 2010, 30(1): 71-85.

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