On a stronger-than-best property for best prediction

On a stronger-than-best property for best prediction

Teunissen, P.J.G.

Aerospace Engineering

Delft Institute for Earth Observation and Space Systems (DEOS)

2007-08-17

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.

Minimum mean squared error (MMSE) prediction
Least-squares collocation
Universal Kriging
Best linear unbiased prediction (BLUP)
Maximum probability of bounded prediction error

http://resolver.tudelft.nl/uuid:9f931556-f3cf-45f0-b92f-ebcf4af8abc7

Springer

1432-1394

Journal of Geodesy, 82 (3)

Institutional Repository

journal article

(c) 2007 The Author; Springer