因变量缺失下部分线性变系数变量含误差模型的估计

数学物理学报 ›› 2010, Vol. 30 ›› Issue (4): 1042-1054.

因变量缺失下部分线性变系数变量含误差模型的估计

魏传华

中央民族大学理学院统计学系北京 100081

收稿日期:2008-08-20 修回日期:2009-10-11 出版日期:2010-07-25 发布日期:2010-07-25
基金资助:
国家社科基金(07CTJ003)和中央民族大学``211工程''项目(021211030312)资助

Estimation in Partially Linear Varying-Coefficient Errors-in-Variables Models with Missing Responses

WEI Chuan-Hua

Department of Statistics, School of Science, |Minzu University of China, Beijing |100081

Received:2008-08-20 Revised:2009-10-11 Online:2010-07-25 Published:2010-07-25
Supported by:
国家社科基金(07CTJ003)和中央民族大学``211工程''项目(021211030312)资助

摘要/Abstract

摘要：

该文主要考虑部分线性变系数模型在自变量含有测量误差以及因变量存在缺失情形下的估计问题. 基于Profile 最小二乘技术, 针对参数分量和非参数分量提出了多种估计方法. 第一种估计方法只利用了完整观测数据, 而第二种和第三种估计方法分别利用了插补技术和替代技术. 参数分量的所有估计被证明是渐近正态的, 非参数分量的所有估计被证明和一般非参数回归函数的估计具有相同的收敛速度. 对于因变量的均值, 构造了两类估计并证明了它们的渐近正态性. 最后, 通过数值模拟验证了所提方法.

关键词: 部分线性变系数模型, 变量含误差, 缺失数据, Profile 最小二乘, 渐近正态

Abstract:

This paper considers the estimation of partially linear varying-coefficient models, which are useful extensions of varying coefficient models and partially linear models. The author focuses on the case where some covariates are measured with additive errors and the response variable is sometime missing. A class of estimators for the parametric component as well as nonparametric components based on the profile least-squares approach are proposed. The first estimator is constructed by using complete-case observations only, the other two by using simple imputation or replacement techniques respectively to complete the sample. All the proposed estimators for the parametric component are shown to be asymptotically normal, and the estimators of nonparametric component achieve the optimal strong convergence rate of the usual nonparametric regression. For the mean of response variable, two estimators are constructed and their asymptotic normalities are established. Simulation studies are conducted to illustrate the approach.

Key words: Asymptotic normality, Measurement error, Missing data, Partially linear varying-coefficient model, Profile least-squares approach

中图分类号:

62J99

魏传华. 因变量缺失下部分线性变系数变量含误差模型的估计[J]. 数学物理学报, 2010, 30(4): 1042-1054.

WEI Chuan-Hua. Estimation in Partially Linear Varying-Coefficient Errors-in-Variables Models with Missing Responses[J]. Acta mathematica scientia,Series A, 2010, 30(4): 1042-1054.

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