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关于回归模型的参数估计效率
引用本文:王正明,周海银.关于回归模型的参数估计效率[J].数学的实践与认识,1999,29(4):64-68.
作者姓名:王正明  周海银
作者单位:国防科技大学数学系,长沙,410073
基金项目:本文承国家自然科学基金资助(69872039),湖南省自然科学基金资助
摘    要:本文讨论回归模型的参数估计效率。本文说明了现有线性回归模型的参数估计效率的下界与真实的参数估计效率在很多情况下相差较大,而且这种下界对于实测数据处理很难得到精确值。本文给出了估算参数估计效率的仿真方法。理论分析表明,该方法给出的参数估计效率的估计较现有的下界估计更合理;仿真和实算结果表明,对于一大类线性和非线性回归模型,该方法给出的回归模型的参数估计效率的估计更接近模型参数估计效率的真值。

关 键 词:回归模型  参数估计效率  仿真方法
修稿时间:1997-11-21

On The Efficiency of Estimation of Parameters of Regression Model
Wang Zhengming,Zhou Haiyin.On The Efficiency of Estimation of Parameters of Regression Model[J].Mathematics in Practice and Theory,1999,29(4):64-68.
Authors:Wang Zhengming  Zhou Haiyin
Institution:Wang Zhengming; (Dept.of Math.,National University of Defense Technology,Changsha
Abstract:Up today the estimator of the lower-bound of the estimation efficiency of parameters of a linear regression model relies on the eigenvalues of the covariance matrix of measuring error vectors. In this paper, we study the difference of this estimation of the lower-bound and the real value of the estimation efficiency and give an artificial algorithm of the estimation efficiency. Theoretical analysis confirms that our efficiency estimator is more reasonable than the traditional lower-bound. Simulation results and real measuring data calculations show that the precision estimation efficiency can be obtained by our method for a large class of linear and nonlinear regression models.
Keywords:Regression model  the estimation efficiency of parameter  artificial algorithm
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