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Conditional versus unconditional mean‐squared prediction errors for Gaussian processes with constant but unknown mean
Author(s) -
Cullmann Andreas Dominik,
Saborowski Joachim
Publication year - 2010
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.1015
Subject(s) - mean squared error , kriging , mathematics , statistics , covariance , conditional variance , conditional expectation , gaussian , mean squared prediction error , variance (accounting) , mean absolute error , ordinary least squares , regression , econometrics , autoregressive conditional heteroskedasticity , volatility (finance) , physics , accounting , quantum mechanics , business
For prediction in a Gaussian random field, we give an explicit formulation of the conditional mean‐squared prediction error (cmspe). If the prediction method is ordinary kriging, we find that this error in most applications is likely to be very close to the ordinary kriging variance. This is additionally demonstrated based on a case study. Finally, we discuss the difference between these two errors compared to the error introduced by using estimated instead of true covariance parameters. Copyright © 2009 John Wiley & Sons, Ltd.