ABSTRACT
This chapter investigates some special topics associated with additive models and nonparametric regression. These include resistant fitting, parametric additive model fitting using regression splines and ridge regression, model selection, and exploration of interactions. The goal of resistant fitting methods is to reduce the influence of outlying points on the estimated model. The object of resistant fitting is to ensure that the estimates are not unduly influenced by a small number of data points. Much has been written on diagnostics and influence measures for smoothing splines and related problems. The Multivariate adaptive regression splines (MARS) procedure has yet to endure the tests of time; it nevertheless seems extremely promising as an automatic high dimensional smoother. It also serves well as a continuous generalization of the regression-tree technology. MARS builds up its tensor-product basis in an adaptive way, and in so doing adds an important dimension to TURBO.
