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.

中文翻译：

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超高维广义变系数模型中的特征筛选


广义变系数模型对于检查协变量对连续、二元或计数响应的动态影响特别有用。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准似然性，因此与文献中提出的边际筛选程序不同。特别是，所提出的程序可以有效地识别与响应共同依赖但略微独立的主动预测变量。为了执行所提出的过程，我们提出了一种有效的算法并建立了所提出算法的上升特性。我们进一步证明所提出的程序具有确定的筛选特性。也就是说，当概率趋于 1 时，所选变量集包括实际的主动预测变量。我们检查了所提出的程序的有限样本性能，并通过蒙特卡罗模拟将其与现有程序进行比较，并通过真实的数据示例说明了所提出的程序。