多维线性回归有偏子模型的多步调整相合推断

数学物理学报 ›› 2012, Vol. 32 ›› Issue (6): 1019-1031.

• 论文 • 下一篇

多维线性回归有偏子模型的多步调整相合推断

曾云辉^1,2|林路¹|王秀丽^1,3

1.山东大学数学学院济南 250100|2.山东省计算中心济南 250014|3.山东师范大学数学科学学院济南 250014

收稿日期:2011-11-25 修回日期:2012-10-12 出版日期:2012-12-25 发布日期:2012-12-25
基金资助:
国家自然科学基金(10921101, 11171188)和山东省自然科学基金(ZR2010AZ001, ZR2011AQ007)资助

Multi-Step-Adjustment Consistent Inference for Biased Sub-Model of Multidimensional Linear Regression

ZENG Yun-Hui^1,2, LIN Lu¹, WANG Xiu-Li^1,3

1.School of Mathematical Science, Shandong University, Jinan 250100|2.Shandong Computer Science Center, Jinan 250014;
3.School of Mathematical Science, Shandong Normal University, Jinan 250014

Received:2011-11-25 Revised:2012-10-12 Online:2012-12-25 Published:2012-12-25
Supported by:
国家自然科学基金(10921101, 11171188)和山东省自然科学基金(ZR2010AZ001, ZR2011AQ007)资助

摘要/Abstract

摘要：

当协变量是高维时经常采用一个子模型作为工作模型. 由于没有包含所有相关的变量, 这个模型可能是有偏的. 这样, 基于子模型得到的参数估计可能是不相合的. 在这篇文章中将首先通过多步调整方法构造一个条件无偏模型. 与现有的方法相比, 这个调整模型仅采用了一维非参估计. 然后得到子模型参数的一个全局相合估计, 而且获得了该估计的渐近正态性. 数值模拟结果显示, 基于调整模型的参数估计优于基于子模型和全模型的参数估计.

关键词: 线性回归, 有偏子模型, 相合估计, 主成分回归;独立成分分析

Abstract:

When the dimension of covariate is high, one usually uses a sub-model as working model. Such a model may be biased because not all relevant variables are contained in it. Thus the resulting estimator of parameter in the sub-model may be inconsistent. In this paper, we shall construct a conditionally unbiased model by multi-step-adjustment. Compared with the existing methods, the adjusted model only adopts univariate nonparametric estimations. A globally consistent estimator of parameter in the sub-model is constructed, and its asymptotic normality is also obtained. The simulation results further illustrate that the performance of the estimator based on the adjusted model is better than those of the estimators derived from the sub-model and the full model.

Key words: Linear regression, Biased sub-model, Consistent estimation, Principal component regression, Independent component analysis

中图分类号:

62F10

曾云辉, 林路, 王秀丽. 多维线性回归有偏子模型的多步调整相合推断[J]. 数学物理学报, 2012, 32(6): 1019-1031.

ZENG Yun-Hui, LIN Lu, WANG Xiu-Li. Multi-Step-Adjustment Consistent Inference for Biased Sub-Model of Multidimensional Linear Regression[J]. Acta mathematica scientia,Series A, 2012, 32(6): 1019-1031.

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多维线性回归有偏子模型的多步调整相合推断

Multi-Step-Adjustment Consistent Inference for Biased Sub-Model of Multidimensional Linear Regression

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