Yang Guangren, Yang Songshan, Li Runze
Jinan University.
Pennsylvania State University.
Stat Sin. 2020;30:1049-1067. doi: 10.5705/ss.202017.0362.
Generalized varying coefficient models are particularly useful for examining dynamic effects of covariates on a continuous, binary or count response. This paper is concerned with feature screening for generalized varying coefficient models with ultrahigh dimensional covariates. The proposed screening procedure is based on joint quasi-likelihood of all predictors, and therefore is distinguished from marginal screening procedures proposed in the literature. In particular, the proposed procedure can effectively identify active predictors that are jointly dependent but marginally independent of the response. In order to carry out the proposed procedure, we propose an effective algorithm and establish the ascent property of the proposed algorithm. We further prove that the proposed procedure possesses the sure screening property. That is, with probability tending to one, the selected variable set includes the actual active predictors. We examine the finite sample performance of the proposed procedure and compare it with existing ones via Monte Carlo simulations, and illustrate the proposed procedure by a real data example.
广义变系数模型对于研究协变量对连续、二元或计数响应的动态效应特别有用。本文关注具有超高维协变量的广义变系数模型的特征筛选。所提出的筛选程序基于所有预测变量的联合拟似然，因此与文献中提出的边际筛选程序不同。特别地，所提出的程序可以有效地识别那些联合依赖但边际上与响应独立的活跃预测变量。为了实施所提出的程序，我们提出了一种有效的算法，并建立了该算法的上升性质。我们进一步证明所提出的程序具有确定筛选性质。也就是说，随着概率趋于1，所选变量集包含实际的活跃预测变量。我们通过蒙特卡罗模拟检验了所提出程序的有限样本性能，并将其与现有程序进行比较，并用一个实际数据例子说明了所提出的程序。
