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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (2): 241-252    
    
单调缺失机制下高维纵向线性回归模型的变量选择
汤杨冰, 田瑞琴, 徐登可
浙江农林大学 统计系, 浙江杭州 311300
Variable selection for high-dimensional longitudinal linear regression models with monotone missing patterns
TANG Yang-bing, TIAN Rui-qin, XU Deng-ke
Department of Statistics, Zhejiang Agriculture and Forestry University, Hangzhou 311300, China
 全文: PDF 
摘要： 在响应变量带有单调缺失的情形下考虑高维纵向线性回归模型的变量选择. 主要基于逆概率加权广义估计方程提出了一种自动的变量选择方法, 该方法不使用现有的惩罚函数, 不涉及惩罚函数非凸最优化的问题, 并且可以自动地剔除零回归系数, 同时得到非零回归系数的估计. 在一定正则条件下, 证明了该变量选择方法具有Oracle性质. 最后, 通过模拟研究验证了所提出方法的有限样本性质.
关键词： 纵向数据;  广义估计方程;  单调缺失;  变量选择;  逆概率加权    
Abstract: This paper considers the problem of variable selection in high-dimensional longitudinal linear regression models with monotone missing patterns. A new variable selection procedure is proposed based on the smooth-threshold inverse probability weighted generalized estimating equation. The proposed procedure avoids the convex optimization problem without using penalty functions. Besides, the proposed method can automatically eliminate inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimate the nonzero regression coefficients. Under some regularity conditions, the variable selection procedure is proved to have Oracle property. Finally, some simulation studies are conducted to examine the finite sample property of the proposed variable selection procedure.
Key words: longitudinal data    generalized estimating equation    monotone missing    variable selection    inverse probability weighted
收稿日期: 2016-05-26 出版日期: 2017-06-01
基金资助: 浙江省自然科学基金(LQ15A010008,LY17A010026); 全国统计科学研究项目(2016LZ06); 浙江省统计研究课题(20150616)
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汤杨冰
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引用本文:

汤杨冰, 田瑞琴, 徐登可. 单调缺失机制下高维纵向线性回归模型的变量选择[J]. 高校应用数学学报, 2017, 32(2): 241-252.

TANG Yang-bing, TIAN Rui-qin, XU Deng-ke. Variable selection for high-dimensional longitudinal linear regression models with monotone missing patterns. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 241-252.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I2/241

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