Song Rui, Yi Feng, Zou Hui
North Carolina State University and University of Minnesota.
Stat Sin. 2014;24(4):1735-1752.
Varying coefficient models have been widely used in longitudinal data analysis, nonlinear time series, survival analysis, and so on. They are natural non-parametric extensions of the classical linear models in many contexts, keeping good interpretability and allowing us to explore the dynamic nature of the model. Recently, penalized estimators have been used for fitting varying-coefficient models for high-dimensional data. In this paper, we propose a new computationally attractive algorithm called IVIS for fitting varying-coefficient models in ultra-high dimensions. The algorithm first fits a gSCAD penalized varying-coefficient model using a subset of covariates selected by a new varying-coefficient independence screening (VIS) technique. The sure screening property is established for VIS. The proposed algorithm then iterates between a greedy conditional VIS step and a gSCAD penalized fitting step. Simulation and a real data analysis demonstrate that IVIS has very competitive performance for moderate sample size and high dimension.
变系数模型已广泛应用于纵向数据分析、非线性时间序列、生存分析等领域。在许多情况下，它们是经典线性模型自然的非参数扩展，保持了良好的可解释性，并使我们能够探索模型的动态性质。最近，惩罚估计器已被用于拟合高维数据的变系数模型。在本文中，我们提出了一种新的具有计算吸引力的算法，称为IVIS，用于拟合超高维变系数模型。该算法首先使用一种新的变系数独立性筛选（VIS）技术选择的协变量子集来拟合一个gSCAD惩罚变系数模型。为VIS建立了确定筛选性质。然后，所提出的算法在贪婪条件VIS步骤和gSCAD惩罚拟合步骤之间进行迭代。模拟和实际数据分析表明，对于中等样本量和高维情况，IVIS具有非常有竞争力的性能。
