Abstract: We consider the nonparametric two-way interaction model and propose a method to select important main effect and interaction effect terms simultaneously. Our method is based on backfitting local constant smoothing. Interaction selection is achieved by solving a constrained optimization problem to identify which main effect and interaction effect terms favor an infinity smoothing bandwidth. We establish the selection consistency for the proposed method. Simulation examples and a real-data example illustrate its competitive finite-sample performance.

Key words and phrases: Additive model, backfitting, local constant smoothing, variable selection.