A framework to understand the asymptotic properties of Kriging and splines

AMS Citation:
Furrer, E. M., and D. Nychka, 2007: A framework to understand the asymptotic properties of Kriging and splines. Journal of the Korean Statistical Society, 36, 57-76,.
Date:2007-01-01
Resource Type:article
Title:A framework to understand the asymptotic properties of Kriging and splines
Abstract: Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given for one dimensional corresponding Mat´ern covariances that have as their limit cubic splines.
Subject(s):Equivalent kernel, Spline, Kriging
Peer Review:Refereed
Copyright Information:Copyright 2007 Korean Statistical Society.
OpenSky citable URL: ark:/85065/d70v8fbn
Author(s):
  • Eva Furrer - NCAR/UCAR
  • Doug Nychka - NCAR/UCAR
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