带线性约束的回归模型参数的Liu估计方法

黄文焕;戚佳金;黄南天

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (7) : 937-946.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (7) : 937-946. DOI: 10.12341/jssms08429
论文

带线性约束的回归模型参数的Liu估计方法

    黄文焕(1), 戚佳金(2), 黄南天(3)
作者信息 +

Liu-Type Estimation for the Linear Model with Linear Restrictions

    HUANG Wenhuan(1), QI Jiajin(2), HUANG Nantian(3)
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摘要

针对一般带约束的最小二乘估计(ORLSE)在参数估计中处理复共线性的不足,通过引入附加随机线性约束,提出了约束Liu型估计方法.经理论证明,此方法在均方误差下较已经提出的ORLSE和约束岭估计(RRE)效果更好,并且它可以作为两种方法的推广形式.讨论了其中k, d的确定原则,并将此方法推广到了广义形式和典则形式下的估计公式.

Abstract

For the multicollinearity in restricted linear regression, there are some problems still left open in current popular ordinary restricted least square estimation. By introducing stochastic linear restrictions, a restricted Liu-type estimation is proposed, which generalizes the ordinary restricted least square estimation and restricted ridge estimation. Then the selection method of the scalars k and d is disscussed and is generalized to the estimation of restricted linear model and canonical form.

关键词

线性回归 / 复共线性 / Liu型估计 / 均方误差.

Key words

Linear regression / multicollinearity / Liu-type estimation / mean squared error.

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黄文焕 , 戚佳金 , 黄南天. 带线性约束的回归模型参数的Liu估计方法. 系统科学与数学, 2009, 29(7): 937-946. https://doi.org/10.12341/jssms08429
HUANG Wenhuan , QI Jiajin , HUANG Nantian. Liu-Type Estimation for the Linear Model with Linear Restrictions. Journal of Systems Science and Mathematical Sciences, 2009, 29(7): 937-946 https://doi.org/10.12341/jssms08429
中图分类号： 62J07    62J05    62C12   
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