北京航空航天大学学报 ›› 2019, Vol. 45 ›› Issue (10): 1990-1994.doi: 10.13700/j.bh.1001-5965.2019.0157

• 论文 • 上一篇    下一篇

含函数型自变量回归模型中的变量选择

刘科生1, 王思洋2   

  1. 1. 北京航空航天大学 学生大数据中心, 北京 100083;
    2. 中央财经大学 统计与数学学院, 北京 100081
  • 收稿日期:2019-04-11 出版日期:2019-10-20 发布日期:2019-10-31
  • 通讯作者: 王思洋 E-mail:siyangw@163.com
  • 作者简介:刘科生 男,博士研究生,助理研究员。主要研究方向:教育大数据、复杂数据分析;王思洋 女,博士,副教授,硕士生导师。主要研究方向:高维数据分析、信用风险建模。
  • 基金资助:
    国家自然科学基金(11501586,71420107025);中央财经大学科研创新团队支持计划

Variable selection in regression models including functional data predictors

LIU Kesheng1, WANG Siyang2   

  1. 1. Big Data Center of Student Affairs Department, Beihang University, Beijing 100083, China;
    2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
  • Received:2019-04-11 Online:2019-10-20 Published:2019-10-31
  • Supported by:
    National Natural Science Foundation of China (11501586,71420107025); Program for Innovation Research in Central University of Finance and Economics

摘要: 针对含有函数型和多元向量数据的回归模型中变量选择和参数估计问题进行研究,扩展了函数型数据分析和变量选择方法的应用范围。首先,函数型自变量基于函数型主成分基函数空间进行投影;然后,对投影后的函数型自变量(按组)及多元向量自变量采用惩罚变量选择方法,同时估计相应的系数。惩罚项调节参数采用自适应调节参数,损失函数采用中位绝对损失函数,以此为例,通过引入松弛变量将估计算法转化为求解线性规划问题,算法复杂度低。数值模拟结果表明,所提方法对于含函数型自变量回归模型的变量选择和参数估计均具有良好效果。

关键词: 函数型数据, 变量选择, 参数估计, 分位数, 函数型主成分

Abstract: The variable selection and parameter estimation problem is researched in the framework of mixed-type regression model with both functional and multivariate predictors, which broadens the scope of functional data analysis and the application fields of variable selection methodology. First the functional predictors are projected into spaces spanned by functional principal component basis functions. Then variable selection and parameter estimation are implemented simultaneously for the multivariate predictors and derived projection predictors in the form of grouping, where the tuning parameter of the penalized term is adaptively selected and the loss function is based on absolute median loss function. As to the optimization procedure, by introducing slack variables, it is transformed into a linear programming problem with several constraint conditions, which simplifies the computation. The simulation results illustrate that the proposed method performs quite well in variable selection and parameter estimation in the mixed-type regression model.

Key words: functional data, variable selection, parameter estimation, quantile, functional principal component

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