Abstract
A weighted cross-validation technique known in the spline literature as generalized cross-validation (GCV), is proposed for covariance model selection and parameter estimation. Weights for prediction errors are selected to give more importance to a cluster of points than isolated points. Clustered points are estimated better by their neighbors and are more sensitive to model parameters. This rational weighting scheme also provides a simplifying significantly the computation of the cross-validation mean square error of prediction. With small- to medium-size datasets, GCV is performed in a global neighborhood. Optimization of usual isotropic models requires only a small number of matrix inversions. A small dataset and a simulation are used to compare performances of GCV to ordinary cross-validation (OCV) and least-squares filling (LS).
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Marcotte, D. Generalized cross-validation for covariance model selection. Math Geol 27, 659–672 (1995). https://doi.org/10.1007/BF02093906
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DOI: https://doi.org/10.1007/BF02093906