Confidence Band for Additive Regression Model

Additive model has been widely recognized as an effective tool for dimension reduction. Existing methods for estimation of additive regression function, including backfitting, marginal integration, projection and spline methods, do not provide any level of uniform confidence. In this paper we propose a simple construction of confidence band for the additive regression function which is based on direct implementation of polynomial spline estimation and wild bootstrap. Monte Carlo results show that the proposed band possesses three desirable properties: excellent coverage of the true function, its width rapidly shrinks to zero with increasing sample size, and its computing time is minimal. Based on these observations, the procedure is highly recommended for nonparametric regression with confidence when additive modelling is appropriate.