Feature screening in ultrahigh-dimensional generalized varying-coefficient models

Generalized varying-coefficient models are particularly useful for examining the dynamic effects of covariates on a continuous, binary, or count response. This study examines feature screening for generalized varying-coefficient models with ultrahigh-dimensional covariates. The proposed screening procedure is based on the joint quasi-likelihood of all predictors, which differentiates it from the marginal screening procedures proposed in the literature. In particular, the proposed procedure effectively identifies active predictors that are jointly dependent, but marginally independent of the response. We provide an algorithm for the proposed procedure, and establish the ascent property of the proposed algorithm. Furthermore, we 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 that of several Monte Carlo simulations. Lastly, we illustrate our procedure using a real-data example.