Generalized cross-validation for covariance model selection |
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| Authors: | Denis Marcotte |
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| Institution: | (1) Mineral Engineering, École Polytechnique, Succ. Centre-ville, C.P. 6079, H3C-3A7 Montréal, Canada |
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| 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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| Keywords: | cross-validation generalized cross-validation covariance model parameter estimation |
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