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含函数型自变量回归模型中的变量选择

刘科生 王思洋

刘科生, 王思洋. 含函数型自变量回归模型中的变量选择[J]. 北京航空航天大学学报, 2019, 45(10): 1990-1994. doi: 10.13700/j.bh.1001-5965.2019.0157
引用本文: 刘科生, 王思洋. 含函数型自变量回归模型中的变量选择[J]. 北京航空航天大学学报, 2019, 45(10): 1990-1994. doi: 10.13700/j.bh.1001-5965.2019.0157
LIU Kesheng, WANG Siyang. Variable selection in regression models including functional data predictors[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(10): 1990-1994. doi: 10.13700/j.bh.1001-5965.2019.0157(in Chinese)
Citation: LIU Kesheng, WANG Siyang. Variable selection in regression models including functional data predictors[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(10): 1990-1994. doi: 10.13700/j.bh.1001-5965.2019.0157(in Chinese)

含函数型自变量回归模型中的变量选择

doi: 10.13700/j.bh.1001-5965.2019.0157
基金项目: 

国家自然科学基金 11501586

国家自然科学基金 71420107025

中央财经大学科研创新团队支持计划 

详细信息
    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

    通讯作者:

    王思洋, E-mail: siyangw@163.com

  • 中图分类号: O212

Variable selection in regression models including functional data predictors

Funds: 

National Natural Science Foundation of China 11501586

National Natural Science Foundation of China 71420107025

Program for Innovation Research in Central University of Finance and Economics 

More Information
  • 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。

     

  • 表  1  正态误差下的数据模拟结果

    Table  1.   Data simulation results with normal error

    (n, σ) 统计指标 TP FP RMSE Bias
    (100, 0.05) Mean 2 0.22 0.028 2 0.005 8
    Sd 0 0.52 0.007 6 0.004 4
    (100, 0.2) Mean 2 0.34 0.084 4 0.022 9
    Sd 0 0.61 0.033 0 0.017 9
    (300, 0.05) Mean 2 0.09 0.016 8 0.002 7
    Sd 0 0.30 0.004 8 0.002 0
    (300, 0.2) Mean 2 0.18 0.049 1 0.012 0
    Sd 0 0.42 0.019 5 0.009 8
    下载: 导出CSV

    表  2  柯西误差下的数据模拟结果

    Table  2.   Data simulation results with Cauchy error

    (n, σ) 统计指标 TP FP RMSE Bias
    (100, 0.05) Mean 2 0.01 0.036 0 0.008 3
    Sd 0 0.07 0.007 6 0.004 4
    (100, 0.2) Mean 2 0.03 0.116 8 0.035 5
    Sd 0 0.16 0.054 7 0.030 1
    (300, 0.05) Mean 2 0 0.019 5 0.003 8
    Sd 0 0 0.006 5 0.002 8
    (300, 0.2) Mean 2 0.12 0.062 1 0.014 0
    Sd 0 0.32 0.026 6 0.011 6
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-04-11
  • 录用日期:  2019-04-26
  • 刊出日期:  2019-10-20

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