北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (6): 792-796.doi: 10.13700/j.bh.1001-5965.2013.0409

• 论文 • 上一篇    下一篇

连续谱数据的函数型主成分回归

黄乐乐1, 王惠文1, 朱嘉2   

  1. 1. 北京航空航天大学 经济管理学院, 北京 100191;
    2. 北京师范大学 化学学院, 北京 100875
  • 收稿日期:2013-07-02 出版日期:2014-06-20 发布日期:2014-07-03
  • 作者简介:黄乐乐(1986- ),男,河南济源人,博士生,nanhuabiren@163.com.
  • 基金资助:

    国家自然科学基金资助项目(71031001,20903013);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)

Functional principal component regression for continuous spectra data

Huang Lele1, Wang Huiwen1, Zhu Jia2   

  1. 1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. College of Chemistry, Beijing Normal University, Beijing 100875, China
  • Received:2013-07-02 Online:2014-06-20 Published:2014-07-03

摘要: 对连续谱数据不做离散化处理,而是将光滑后的连续谱作为连续曲线,进行函数型主成分回归分析,以期获得既可降维又能减少信息损失的回归方程.在此建模过程中,还引入连续谱的导数曲线作为协变量,并给出函数型主成分回归系数的bootstrap置信区间.作为实证研究,对玻璃样品的X射线谱和样品中硅元素含量进行回归分析.研究结果表明,基于函数型主成分的回归分析对响应变量具有较强解释能力,同时其回归系数更加符合数据本身的特点,显示出新方法所具有的优越性与实用价值.

Abstract: The method treating the smooth spectra as functional data was proposed and regression analysis was carried out based on functional principal components of spectra curves to obtain regression models without discretization. In modeling, the derivative curves of spectra can be introduced and bootstrap confidence intervals for functional coefficients were obtained. Using this method, the regression relationship between element concentration and X-ray spectra of glass samples was analyzed. It is shown that the functional regression based on principal components is more acceptable and has many advantages, because it complies with the characteristics of the data itself while attaining strong explanatory ability.

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