ABSTRACT
This chapter examines model set-up and estimation given smoothing parameters. It discusses smoothing parameter estimation criteria, and introduces the computational methods for efficiently optimizing these criteria. The chapter describes the results needed for further inference and model selection, and explains interval estimation and posterior simulation. Leave-several-out cross validation can be used, and again only a single model fit is needed for the computations. Ordinary cross validation (OCV) is a reasonable way of estimating smoothing parameters, but suffers from two potential drawbacks. Firstly, it is computationally expensive to minimize in the additive model case, where there may be several smoothing parameters. Secondly, it has a slightly disturbing lack of invariance. There are a number of ways of producing smoothing parameter selection criteria for the generalized case, which essentially substitute the model deviance or the Pearson statistic for the residual sum of squares in the UBRE score or the GCV score.
