SPLINES - MORE THAN JUST A SMOOTH INTERPOLATOR

Minimum cross validation thin plate smoothing splines are easy to use. They are approximately as accurate for interpolation as kriging, but avoid initial estimation of the covariance structure. Their smoothing properties suggest a natural parallel with the version of kriging where the nugget variance is interpreted as measurement error, so that there are no singularities at the data points. Both methods are then seen to be estimators of the underlying spatially coherent signal which filter out the discontinuous nugget error. They give rise to a simple procedure for outlier detection, and there are natural analogues between the various statistics associated with each method. The trace of the influence matrix is shown to provide useful diagnostic information about the fitted spline. The connection between the structural analysis of universal kriging and the choice of the order of the derivative minimized by thin plate splines is demonstrated by analyzing data. It is suggested that the generalized cross validation calculated for splines may be a more reliable measure of overall prediction error than the variogram dependent predictive error calculated for kriging. Further examples confirm published results which show that the interpolation accuracies of thin plate splines and well parameterized kriging analyses are similar at larger spacings. Computational procedures for splines and kriging are discussed, and some generalizations of thin plate splines are briefly described.