Table of Contents#### Download Safari Books Online apps: Apple iOS | Android | BlackBerry

Entire Site

Free Trial

Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.

588 Introduction to Robust Estimation and Hypothesis Testing tests the hypothesis given by Eq. (11.17). If xout=T, outliers among the x values are first identified and (y i , x i ) is eliminated if x i is flagged an outlier. 11.6.5 Inferences About the Components of a Generalized Additive Model Inferences about the components of a generalized additive model, based on the running interval smoother, can be made as follows. For convenience, assume the goal is to test H 0 : g 1 (x 1 ) = 0. Fit the generalized additive model yielding y i = b 0 + g 2 (x i2 ) + · · · + g p (x i p ). ^ ^ ^ Let r i = y i - y i , i = 1, . . . , n. The strategy is to test the hypothesis that the association ^ between the residuals and x 1 is a straight horizontal line, and this can be done with the wild bootstrap method in Section 9.5 (cf. H ardle & Korostelev, 1996). ¨ When using the running interval smoother, the choice of the span can be crucial in terms of controlling the probability of a type I error (Wilcox, 2006a). Letting f be the span used in Section 11.5.4. The choice for f when using means or a 20% trimmed mean are as follows: