Confidence Band for Additive Regression Model

Abstract

Additive model is 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 a simple construction of confidence band is proposed for the additive regression function based on polynomial spline estimation and wild bootstrap. Monte Carlo results show three desirable properties of the proposed band: excellent coverage of the true function, width rapidly shrinking to zero with increasing sample size, and minimal computing time. These properties make he procedure is highly recommended for nonparametric regression with confidence when additive modelling is appropriate.