ABSTRACT
In the last chapter, it was demonstrated how the problem of estimating a generalized
additive model becomes the problem of estimating smoothing parameters and model
coefficients for a penalized likelihood maximization problem, once a basis for the
smooth functions has been chosen, together with associated measures of function
wiggliness. In practice the penalized likelihood maximization problem is solved by
penalized iteratively re-weighted least squares (P-IRLS), while the smoothing pa-
rameters can be estimated using cross validation or related criteria. The purpose of
this chapter is to justify and extend the methods introduced in chapter 3, and to add
some distribution theory to facilitate confidence interval calculation and hypothesis
testing. Table 4.1 lists the main elements of the approach, and where they can be
found within the chapter.
