纵向数据下变系数线性模型的惩罚秩回归
Penalized Rank Regression for Varying-Coefficient Linear Models with Longitudinal Data
摘要: 针对纵向数据变系数线性模型中数据具有组内相关性和组间独立性，以及组内协方差矩阵估计效率低的特点，本文基于修正的Cholesky分解和B样条函数处理非参数部分，对组内协方差矩阵提出更有效的估计，改善了不平衡纵向数据的估计效率。同时，文章结合了两个非凸惩罚函数SCAD和MCP实现稳健的变量选择，模拟研究和实证分析表明新方法能够获得更有效的估计，并且相同参数准则下，对高相关性的样本数据，MCP惩罚函数的显著性更强。
Abstract: For longitudinal data in varying coefficient linear models characterized by within-group correlation and between-group independence, as well as the low estimation efficiency of within-group covariance matrices, this paper proposes a more efficient estimation method for the within-group covariance matrix based on modified Cholesky decomposition and B-spline functions to handle the nonparametric components, thereby improving the estimation efficiency for unbalanced longitudinal data. Additionally, the study incorporates two non-convex penalty functions, SCAD and MCP, to achieve robust variable selection. Simulation studies and empirical analyses demonstrate that the proposed method yields more efficient estimates. Under the same parameter criteria, the MCP penalty exhibits stronger significance for highly correlated sample data.
文章引用：张雅斐. 纵向数据下变系数线性模型的惩罚秩回归[J]. 统计学与应用, 2025, 14(7): 334-345. https://doi.org/10.12677/sa.2025.147209

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