FOR HIGH-DIMENSIONAL VARYING-COEFFICIENT MODELS

Abstract: 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. Re-cently, 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 sub-set of covariates selected by a new varying-coefficient independence screening (VIS) technique. The sure screening property is established for VIS. The proposed algo-rithm 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. 1