含高相关协变量的纵向广义线性模型变量选择研究
Variable Selection in Longitudinal Generalized Linear Models with Highly Correlated Covariates
DOI: 10.12677/aam.2024.137303, PDF,    国家社会科学基金支持
作者: 范 涛*：重庆工商大学数学与统计学院，重庆；赵培信：重庆工商大学数学与统计学院，重庆；统计智能计算与检测重庆市重点实验室，重庆
关键词: 广义线性模型；高相关协变量；纵向数据；变量选择；Generalized Linear Models； Highly Correlated Covariates； Longitudinal Data； Variable Selection
摘要: 结合半标准偏协方差函数(SPAC)和Lasso惩罚估计方法，对一类纵向数据下的广义线性模型的变量选择问题提出一种基于SPAC-Lasso惩罚的变量选择方法。在一些正则性条件下证明了所提出的变量选择方法的相合性，并给出了所得正则估计的收敛速度。所提出的变量选择方法允许协变量之间存在高相关性，改进并推广了已有变量选择方法的应用领域。
Abstract: Combining the semi-parametric approximate covariance function (SPAC) and Lasso penalized estimation method, we propose a variable selection approach based on SPAC-Lasso penalty for a class of longitudinal generalized linear models. Under some regularity conditions, we demonstrate the consistency of the proposed variable selection method and provide the convergence rate of the resulting regularized estimates. The proposed variable selection method allows for high correlations among covariates, improving and extending the applicability of existing variable selection methods.
文章引用：范涛, 赵培信. 含高相关协变量的纵向广义线性模型变量选择研究[J]. 应用数学进展, 2024, 13(7): 3175-3181. https://doi.org/10.12677/aam.2024.137303

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