Variable selection in strong hierarchical semiparametric models for longitudinal data.
Variable selection in strong hierarchical semiparametric models for longitudinal data.
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DOI：
10.4310/sii.2015.v8.n3.a9
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发表时间：
2015
影响因子：
0.8
通讯作者：
Li Y
中科院分区：
文献类型：
--
作者：
Zeng X;Ma S;Qin Y;Li Y
本文研究纵向数据半参数可加部分线性模型的变量选择问题。我们的目标是识别与响应变量相关的相关主效应和相应的交互作用。同时，我们对模型实施了强层次限制，即只有当两个关联的主效应都包含时，交互作用才可以包含在模型中。基于非参数分量的B样条基逼近，提出了一种迭代估计方法，通过对似然函数进行部分分组极小极大凹罚（MCP），并利用BIC选择调整参数.为了进一步提高估计效率，我们通过最大似然估计来指定工作协方差矩阵。仿真结果表明，该方法具有一致性，能有效地进行有限样本的估计和预测，特别是当真实模型服从强层次结构时。最后，利用中国股票市场数据对模型进行了拟合，验证了模型的有效性.
In this paper, we consider the variable selection problem in semiparametric additive partially linear models for longitudinal data. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Meanwhile, we enforce the strong hierarchical restriction on the model, that is, an interaction can be included in the model only if both the associated main effects are included. Based on B-splines basis approximation for the nonparametric components, we propose an iterative estimation procedure for the model by penalizing the likelihood with a partial group minimax concave penalty (MCP), and use BIC to select the tuning parameter. To further improve the estimation efficiency, we specify the working covariance matrix by maximum likelihood estimation. Simulation studies indicate that the proposed method tends to consistently select the true model and works efficiently in estimation and prediction with finite samples, especially when the true model obeys the strong hierarchy. Finally, the China Stock Market data are fitted with the proposed model to illustrate its effectiveness.