Journal of statistical planning and inference vol:103 issue:1-2 pages:455-470
Generalized additive models have become one of the most widely used modem statistical tools. Traditionally, they are fit through scatterplot smoothing and the backfitting algorithm. However, a more recent development is the direct fitting through the use of low-rank smoothers (Hastic, J. Roy. Statist. Soc. Ser. B 58 (1996) 379). A particularly attractive example of this is through use of penalized splines (Marx and Eilers, Comput. Statist. Data Anal. 28 (1998) 193). Such an approach has a number of advantages, particularly regarding computation. In this paper, we exploit the explicitness of penalized spline additive models to derive some useful and revealing theoretical approximations. (C) 2002 Elsevier Science B.V. All rights reserved.