Abstract

P.A. Hancock (1) and M.F. Hutchinson (2)

(1) Centre for Resource and Environmental Studies, Email: penleper@cres.anu.edu.au
(2) Centre for Resource and Environmental Studies, Email: hutch@cres.anu.edu.au

This study analyses a simple iterative procedure for estimating minimum generalised cross-validation (GCV) unidimensional smoothing splines. The results provide guidelines for the development of a similar methodology to estimate minimum GCV bivariate thin plate smoothing splines. The methodology is based on techniques described in Hutchinson (2000), which use nested grid SOR iterative methods to solve finite element thin plate smoothing spline systems efficiently for large data sets. A double iteration is used to produce increasingly accurate estimates of the minimum GCV smoothing parameter and update the solution estimate accordingly. First and second derivatives of the GCV with respect to the smoothing parameter are used to update the smoothing parameter. Convergence of the SOR iteration can be improved significantly by correcting the solution estimate after each smoothing parameter update using the estimate of the derivative of the solution with respect to the smoothing parameter.

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