Exponential-bound property of estimators and variable selection in generalized additive models

We discuss the asymptotic property of estimators for generalized additive models based on a marginal integration estimation method introduced by Linton and Nielsen (1995). General results of the mean error exponential bound property are established. Applying these results, a new method for variable selection in generalized additive models is introduced. We directly test if a additive component is significant. We use the wild-bootstrap method (Wu, 1986) for choosing threshold of the test. This procedure is applied to each design variable one at one time. Comparisons are made to demonstrate the practical advantages of the proposed method over the other existing methods.