Cross validation of kriging in a unique neighborhood
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Cross validation is an appropriate tool for testing interpolation methods: it consists of leaving out one data point at a time, and determining how well this point can be estimated from the other data. Cross validation is often used for testing “moving neighborhood” kriging models; in this case, each unknown value is predicted from a small number of surrounding data. In “unique neighborhood” kriging algorithms, each estimation uses all the available data; as a result, cross validation would spend much computer time. For instance, with ndata points it would cost at least the resolution of nsystems of n × nlinear equations (each with a different matrix).Here, we present a much faster method for cross validation in a unique neighborhood. Instead of solving nsystems n × n,it only requires the inversion of one n × nmatrix. We also generalized this method to leaving out several points instead of one.
Key wordscross validation kriging moving neighborhood unique neighborhood
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- Delfiner, P. and Delhomme, J. P., 1973, Optimum interpolation by kriging: Proceedings of NATO-ASI, Display and Analysis of Spatial Data, Nottingham, John Wiley & Sons, New York/London, p. 96–114.Google Scholar
- Dubrule, O., 1981, Krigeage et splines en cartographie automatique—application a des exemples petroliers: Thesis, ENSMP, Centre de Geostatistique, 35 rue St. Honore, Fontainebleau, France, 150 p.Google Scholar
- Journel, A. G. and Huijbregts, Ch. J., 1978, Mining geostatistics: Academic Press, London, 598 p.Google Scholar
- Matheron, G., 1971, The theory of regionalized variables and its applications: les cahiers du CMM, Fasc. 5, ENSMP, Paris, 211 p.Google Scholar