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带线性约束的回归模型参数的Liu估计方法
引用本文: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[J].系统科学与数学,2009,29(7):937-946.
作者姓名:黄文焕  戚佳金  黄南天
作者单位:1. 吉林化工学院,吉林,132022
2. 国家电网杭州市电力局,杭州,310009
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.

关 键 词:线性回归    复共线性    Liu型估计    均方误差.
收稿时间:2007-12-11

LIU-TYPE ESTIMATION FOR THE LINEAR MODEL WITH LINEAR RESTRICTIONS
HUANG Wenhuan,QI Jiajin,HUANG Nantian.LIU-TYPE ESTIMATION FOR THE LINEAR MODEL WITH LINEAR RESTRICTIONS[J].Journal of Systems Science and Mathematical Sciences,2009,29(7):937-946.
Authors:HUANG Wenhuan  QI Jiajin  HUANG Nantian
Institution:(1)Jilin Institute of Chemical Technology, Jilin 132022; (2)Hangzhou Electric Power Bureau, State Grid Corporation of China, Hangzhou 310009; (3)Jilin Institute of Chemical Technology, Jilin 132022.
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.
Keywords:Linear regression  multicollinearity  Liu-type estimation  mean squared error  
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