北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (11): 1487-1491.doi: 10.13700/j.bh.1001-5965.2013.0680

• 论文 • 上一篇    下一篇

多元线性回归模型的增量算法

王惠文, 魏嫄, 黄乐乐   

  1. 北京航空航天大学 经济管理学院, 北京 100191
  • 收稿日期:2013-11-26 出版日期:2014-11-20 发布日期:2014-12-02
  • 通讯作者: 黄乐乐 E-mail:nanhuabiren@163.com
  • 作者简介:王惠文(1957-),女,辽宁大连人,教授,wanghw@vip.sina.com
  • 基金资助:

    国家自然科学基金资助项目(71031001);北京航空航天大学博士研究生创新基金资助项目(YWF-14-YJSY-027);国家高技术研究发展计划资助(SS2014AA012303)

Incremental algorithm of multiple linear regression model

Wang Huiwen, Wei Yuan, Huang Lele   

  1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2013-11-26 Online:2014-11-20 Published:2014-12-02

摘要:

伴随着各领域信息化的发展,数据多呈现出快速、连续流入的特点.面向海量不断更新的数据集,在具有广泛使用价值的线性回归模型中,考虑引入增量算法.通过基于叉积矩阵的增量计算公式,得到最小二乘估计模型的增量算法,并进一步扩展到其他的模型估计量和检验统计量中.该增量算法运用了全部的数据信息,与使用全部数据建模具有完全相同的结果.算法节约了数据读取时间,减小了数据存储传输的压力,从而提高了计算效率.数据仿真实验验证了算法的有效性.

关键词: 线性回归模型, 增量算法, 叉积阵, 估计, 检验

Abstract:

With the development of computer-related technology, people can continuously obtain data faster and faster. Facing with the massive and continuously updated data sets, incremental algorithm was introduced to the popular multiple linear regression analysis. The incremental algorithm of least squares estimation model was derived based on incremental expression of cross product matrix. And further this algorithm was extended to other estimation models and test statistics. The incremental algorithm uses the information of all dataset, which can get the same results with non-incremental methods. This algorithm can save the time in reading and writing data, release the impression on transportation, and thus speed up the computation. Simulation results show that, this algorithm can improve computational efficiency and is very useful in many conditions.

Key words: linear regression model, incremental algorithm, cross product matrix, estimation, test

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