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Kriging prediction intervals based on semiparametric bootstrap
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: Mathematical Geosciences, ISSN 1874-8961, E-ISSN 1874-8953, Vol. 42, no 8, 985-1000 p.Article in journal (Refereed) Published
Abstract [en]

Kriging is a widely used method for prediction, which, given observations of a (spatial) process, yields the best linear unbiased predictor of the process at a new location. The construction of corresponding prediction intervals typically relies on Gaussian assumptions. Here we show that the distribution of kriging predictors for non-Gaussian processes may be far from Gaussian, even asymptotically. This emphasizes the need for other ways to construct prediction intervals. We propose a semiparametric bootstrap method with focus on the ordinary kriging predictor. No distributional assumptions about the data generating process are needed. A simulation study for Gaussian as well as lognormal processes shows that the semiparametric bootstrap method works well. For the lognormal process we see significant improvement in coverage probability compared to traditional methods relying on Gaussian assumptions.

Place, publisher, year, edition, pages
Springer Verlag , 2010. Vol. 42, no 8, 985-1000 p.
National Category
Computational Mathematics Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-37310DOI: 10.1007/s11004-010-9302-9ISI: 000283087600006OAI: oai:DiVA.org:umu-37310DiVA: diva2:359110
Available from: 2010-10-26 Created: 2010-10-26 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Spatial sampling and prediction
Open this publication in new window or tab >>Spatial sampling and prediction
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis discusses two aspects of spatial statistics: sampling and prediction. In spatial statistics, we observe some phenomena in space. Space is typically of two or three dimensions, but can be of higher dimension. Questions in mind could be; What is the total amount of gold in a gold-mine? How much precipitation could we expect in a specific unobserved location? What is the total tree volume in a forest area? In spatial sampling the aim is to estimate global quantities, such as population totals, based on samples of locations (papers III and IV). In spatial prediction the aim is to estimate local quantities, such as the value at a single unobserved location, with a measure of uncertainty (papers I, II and V).

In papers III and IV, we propose sampling designs for selecting representative probability samples in presence of auxiliary variables. If the phenomena under study have clear trends in the auxiliary space, estimation of population quantities can be improved by using representative samples. Such samples also enable estimation of population quantities in subspaces and are especially needed for multi-purpose surveys, when several target variables are of interest.

In papers I and II, the objective is to construct valid prediction intervals for the value at a new location, given observed data. Prediction intervals typically rely on the kriging predictor having a Gaussian distribution. In paper I, we show that the distribution of the kriging predictor can be far from Gaussian, even asymptotically. This motivated us to propose a semiparametric method that does not require distributional assumptions. Prediction intervals are constructed from the plug-in ordinary kriging predictor. In paper V, we consider prediction in the presence of left-censoring, where observations falling below a minimum detection limit are not fully recorded. We review existing methods and propose a semi-naive method. The semi-naive method is compared to one model-based method and two naive methods, all based on variants of the kriging predictor.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2012. 42 p.
Keyword
Auxiliary variables, Censoring, Inclusion probabilities, Kriging, Local pivotal method, Minimum detection limit, Prediction intervals, Representative sample, Spatial process, Spatial sampling, Semiparametric bootstrap
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-53286 (URN)978-91-7459-373-0 (ISBN)
Public defence
2012-04-12, MIT-huset, MA 121, Umeå universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2012-03-22 Created: 2012-03-20 Last updated: 2012-03-20Bibliographically approved

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