北京航空航天大学学报 ›› 2013, Vol. 39 ›› Issue (9): 1259-1262,1268.

• 论文 • 上一篇    下一篇

快速Gram-Schmidt回归方法

王惠文1, 夏棒1, 孟洁2   

  1. 1. 北京航空航天大学 经济管理学院, 北京 100191;
    2. 中央财经大学 统计学院, 北京 102206
  • 收稿日期:2012-11-09 出版日期:2013-09-30 发布日期:2013-10-13
  • 作者简介:王惠文(1957-),女,河北玉田人,教授,wanghw@vip.sina.com.
  • 基金资助:

    国家自然科学基金资助项目(71031001,71001110)

Fast algorithm of Gram-Schmidt regression method

Wang Huiwen1, Xia Bang1, Meng Jie2   

  1. 1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. School of Statistics, Central University of Finance and Economics, Beijing 102206, China
  • Received:2012-11-09 Online:2013-09-30 Published:2013-10-13

摘要: 提出一种快速的变量筛选与回归建模方法.该方法将在建模过程中,一方面筛选出对因变量有最佳解释作用的信息;另一方面基于Gram-Schmidt正交变换,识别和检验模型中的冗余变量,以便能够及时和成批量地删除所有冗余信息.仿真分析指出,在自变量数量巨大,同时变量之间的多重相关程度又非常高的情形下,与经典的逐步回归相比,该方法的计算速度更快,建模过程更加简洁有效.

Abstract: A new multiple linear regression method was proposed which can screen the variables fast. In the modeling process, not only can it screen variables containing best information to explain the dependent variable, but also distinguish and test redundant variables in the model based on Gram-Schmidt orthogonal transformation, so as to timely strike out all the redundant information in quantity. The simulation analysis shows that compared to classic stepwise regression this new method has a higher arithmetic speed and the modeling process is briefer and more efficient, when the variables appear in a large quantity and have a pretty serious server multicollinearity at the same time.

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