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 wher e the nugget variance is interpreted as measurement error, so that the re are no singularities at the data points. Both methods are then seen to be estimators of the underlying spatially coherent signal which fi lter out the discontinuous nugget error. They give rise to a simple pr ocedure 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 abo ut the fitted spline. The connection between the structural analysis o f universal kriging and the choice of the order of the derivative mini mized by thin plate splines is demonstrated by analyzing data. It is s uggested that the generalized cross validation calculated for splines may be a more reliable measure of overall prediction error than the va riogram dependent predictive error calculated for kriging. Further exa mples confirm published results which show that the interpolation accu racies of thin plate splines and well parameterized kriging analyses a re similar at larger spacings. Computational procedures for splines an d kriging are discussed, and some generalizations of thin plate spline s are briefly described.