Abstract: Varying coefficient models have been widely used in longitudinal data analysis, nonlinear time series, survival analysis, and so on. They are natural nonparametric 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.

Key words and phrases: Penalized regression, sure screening property, varying-coefficient models.