Smoothing and interpolation by kriging and with splines

  • G. S. Watson


Let scalar measurements at distinct points x1, ⋯, xnbe y1, ⋯, yn.We may look for a smooth function f(x)that goes through or near the points (xi, yi).Kriging assumes f(x)is a random function with known (possibly estimable) covariance function (in the simplest case). Splines assume a definition of the smoothness of a nonrandom function f(x).An elementary explanation is given of the fact that spline approximations are special cases of the solution of a kriging problem.

Key words

kriging splines interpolation smoothing prediction Green's function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Dubrule, O., 1983, Two methods with different objectives: Splines and Kriging: Jour. Math. Geol., v. 15, p. 245–257.Google Scholar
  2. Huber, A., 1979, Robust smoothing,in R. L. Launer and G. N. Wilkinson (Eds.), Robustness in statistics: Academic Press, New York, p. 296.Google Scholar
  3. Journel, A. and Huijbregts, C. J., 1978, Mining geostatistics: Academic Press, London, p. 600.Google Scholar
  4. Kimeldorf, G. and Wahba, G., 1970, A correspondence between Bayesian estimation of stochastic processes and smoothing by splines: Ann. Math. Stat., v. 41, p. 495–502.Google Scholar
  5. Love, A. E. H., 1944, A treatise on the mathematical theory of elasticity: Dover, New York, p. 643.Google Scholar
  6. Matheron, G., 1965, Les variables régionalisée et leur estimation: Masson, Paris, p. 306.Google Scholar
  7. Matheron, G., 1981, Splines and kriging: Syracuse University, Geol. Contrib., v. 8, p. 77–95.Google Scholar
  8. Prenter, P. M., 1975, Splines and variational methods: John Wiley & Sons, New York, p. 323.Google Scholar
  9. Salkauskas, K., 1982, Some relationships between surface splines and Kriging: Inter. Ser. Num. Math., v. 1, p. 313–325.Google Scholar
  10. Watson, G. S., 1972, Trend surface analysis and spatial correlation: Geol. Soc. Amer., Spec. pap. 146, p. 39–46.Google Scholar
  11. Watson, G. S., to appear, Interpolation and smoothing of directed and undirected datain P. R. Krishnaiah (Ed.), Multivariate analysis VI: Academic Press, New York.Google Scholar
  12. Tapia, R. A. and Thompson, J. R., 1978, Nonparametric probability density estimation: The Johns Hopkins Univ. Press, Baltimore, pp. 176.Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • G. S. Watson
    • 1
  1. 1.Department of StatisticsPrinceton UniversityPrincetonUSA

Personalised recommendations