Local Likelihood Estimation in Generalized Additive Models

Abstract

ABSTRACT. Generalized additive models are a popular class of multivariate non‐parametric regression models, due in large part to the ease of use of the local scoring estimation algorithm. However, the theoretical properties of the local scoring estimator are poorly understood. In this article, we propose a local likelihood estimator for generalized additive models that is closely related to the local scoring estimator fitted by local polynomial regression. We derive the statistical properties of the estimator and show that it achieves the same asymptotic convergence rate as a one‐dimensional local polynomial regression estimator. We also propose a wild bootstrap estimator for calculating point‐wise confidence intervals for the additive component functions. The practical behaviour of the proposed estimator is illustrated through a simulation experiment.