统计研究 ›› 2009, Vol. 26 ›› Issue (6): 92-97.

• 论文 • 上一篇    下一篇

线性GMDH参数模型的无偏估计研究

鲁茂 贺昌政 李慧   

  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2009-06-15 发布日期:2009-06-15

The Linear Unbiasedness Property of Linear GMDH Parametric Model

  • Received:1900-01-01 Revised:1900-01-01 Online:2009-06-15 Published:2009-06-15

摘要: 多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论:一,在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二,在满足其它假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三,用参数GMHD方法建模时,它对完全多重共线性是免疫的。

关键词: 线性GMDH参数模型, 参数估计, 线性无偏估计量

Abstract: It is a important index of the linear unbiasedness property of parameter to measure a parameter estimation method in multiple linear regression. This paper analyses parameters estimation in multiple linear regression based on the linear GMDH parametric model, and there are several conclusions as follows: Firstly, given the assumptions of the classical linear regression model, all estimators are linear unbiasedness estimator. Secondly, given the same assumptions except for this assumption that the number of observations must be greater than the number of parameters to be estimated, all estimators are still linear unbiasedness estimator. Thirdly, the parametric GMDH algorithm is immunity for perfect multicollinearity.

 

Key words: linear GMDH parametric model, parameter estimation, linear unbiasedness estimator