Derivative estimation and testing in generalized additive models

Abstract

Estimation and testing procedures for generalized additive (interaction) model are developed. We present extensions of several existing procedures for additive models when the link is the identity. This set of methods includes estimation of all component functions and their derivatives, testing functional forms and in particular variable selection. Theorems and simulation results are presented for the fundamentally new procedures. These comprise of, in particular, the introduction of local polynomial smoothing for this kind of models and the testing, including variable selection. Our method is straightforward to implement and the simulation studies show good performance in even small data sets.