On a stronger-than-best property for best prediction
The minimum mean squared error (MMSE) criterion is a popular criterion for devising best predictors. In case of linear predictors, it has the advantage that no further distributional assumptions need to be made, other then about the first- and second-order moments. In the spatial and Earth sciences,...
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| Format: | Journal Article |
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Springer - Verlag
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/34386 |
| _version_ | 1848754208650559488 |
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| author | Teunissen, Peter |
| author_facet | Teunissen, Peter |
| author_sort | Teunissen, Peter |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The minimum mean squared error (MMSE) criterion is a popular criterion for devising best predictors. In case of linear predictors, it has the advantage that no further distributional assumptions need to be made, other then about the first- and second-order moments. In the spatial and Earth sciences, it is the best linear unbiased predictor (BLUP) that is used most often. Despite the fact that in this case only the first- and second-order moments need to be known, one often still makes statements about the complete distribution, in particular when statistical testing is involved. For such cases, one can do better than the BLUP, as shown in Teunissen (J Geod. doi: 10.1007/s00190-007-0140-6, 2006), and thus devise predictors that have a smaller MMSE than the BLUP. Hence, these predictors are to be preferred over the BLUP, if one really values the MMSE-criterion. In the present contribution, we will show, however, that the BLUP has another optimality property than the MMSE-property, provided that the distribution is Gaussian. It will be shown that in the Gaussian case, the prediction error of the BLUP has the highest possible probability of all linear unbiased predictors of being bounded in the weighted squared norm sense. This is a stronger property than the often advertised MMSE-property of the BLUP. |
| first_indexed | 2025-11-14T08:36:46Z |
| format | Journal Article |
| id | curtin-20.500.11937-34386 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:36:46Z |
| publishDate | 2008 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-343862019-02-19T04:27:24Z On a stronger-than-best property for best prediction Teunissen, Peter Minimum mean squared error (MMSE) prediction - Least-squares collocation - Universal Kriging - Best linear unbiased prediction (BLUP) - Maximum probability of bounded prediction error The minimum mean squared error (MMSE) criterion is a popular criterion for devising best predictors. In case of linear predictors, it has the advantage that no further distributional assumptions need to be made, other then about the first- and second-order moments. In the spatial and Earth sciences, it is the best linear unbiased predictor (BLUP) that is used most often. Despite the fact that in this case only the first- and second-order moments need to be known, one often still makes statements about the complete distribution, in particular when statistical testing is involved. For such cases, one can do better than the BLUP, as shown in Teunissen (J Geod. doi: 10.1007/s00190-007-0140-6, 2006), and thus devise predictors that have a smaller MMSE than the BLUP. Hence, these predictors are to be preferred over the BLUP, if one really values the MMSE-criterion. In the present contribution, we will show, however, that the BLUP has another optimality property than the MMSE-property, provided that the distribution is Gaussian. It will be shown that in the Gaussian case, the prediction error of the BLUP has the highest possible probability of all linear unbiased predictors of being bounded in the weighted squared norm sense. This is a stronger property than the often advertised MMSE-property of the BLUP. 2008 Journal Article http://hdl.handle.net/20.500.11937/34386 10.1007/s00190-007-0169-6 Springer - Verlag fulltext |
| spellingShingle | Minimum mean squared error (MMSE) prediction - Least-squares collocation - Universal Kriging - Best linear unbiased prediction (BLUP) - Maximum probability of bounded prediction error Teunissen, Peter On a stronger-than-best property for best prediction |
| title | On a stronger-than-best property for best prediction |
| title_full | On a stronger-than-best property for best prediction |
| title_fullStr | On a stronger-than-best property for best prediction |
| title_full_unstemmed | On a stronger-than-best property for best prediction |
| title_short | On a stronger-than-best property for best prediction |
| title_sort | on a stronger-than-best property for best prediction |
| topic | Minimum mean squared error (MMSE) prediction - Least-squares collocation - Universal Kriging - Best linear unbiased prediction (BLUP) - Maximum probability of bounded prediction error |
| url | http://hdl.handle.net/20.500.11937/34386 |