Local Likelihood Estimation in Generalized Additive Models

Generalized additive models are a popular class of multivariate
nonparametric 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 pointwise
confidence intervals for the additive component functions. The
practical behavior of the proposed estimator is illustrated through
simulation experiments and an example.