ABSTRACT

In this chapter we shall consider the extension of the penalized least squares idea to regression in more than one dimension. We shall see that there is a natural generalization of smoothing splines to two or more dimensions and that some, but not all, of the attractive features of spline smoothing in one dimension carry over. The method we shall describe is called thin plate splines, and for further details the reader is referred to Wahba (1990, Section 2.4) and to the references cited there.