ABSTRACT
This chapter describes an additive extension of the family of generalized linear models, another useful class of linear models. It discusses somewhat different method for estimating a generalized additive model, called local-likelihood estimation. In the Gaussian case, local-likelihood estimation is exactly the same as a locally-weighted running-line smoothing. As was the case for the backfitting algorithm, one can motivate the local-scoring procedure in a number of ways. Local-likelihood estimation bears a strong similarity to the local-scoring procedure. Estimation of the link function and score tests for assessing the need for a link function modification were discussed in Pregibon. Nonparametric estimation of the link function is possible, through a Gauss-Newton procedure, leading to a generalized version of the local-scoring procedure. The Average Derivative Estimation technique uses a multivariate density estimate of the predictors to derive an estimate of the link function.
