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Construction of kriging prediction intervals for non-Gaussian spatial processes
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.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this article, we compare three methods to construct prediction intervals for the value of a stationary process, based on plug-in ordinary kriging predictors. Ordinary kriging is a widely used method for prediction that, given observations of a (spatial) process, forms the best linear unbiased predictor of the process at a new location. Construction of prediction intervals for the value of interest based on ordinary kriging predictors typically rely on Gaussian assumptions. Special attention is here given to non-Gaussian processes, where construction of such intervals is less straightforward.  Methods based on asymptotic normality, Gaussian transformations and semiparametric bootstrap are compared on simulated and real data. The study suggests that the semiparametric method (that does not rely on distributional assumptions) is robust and is to be recommended for non-Gaussian processes. For practitioners the semiparametric method is an attractive alternative since the method can be used without spcifying a link function or making distributional assumptions.

National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-53277OAI: oai:DiVA.org:umu-53277DiVA: diva2:511106
Available from: 2012-03-20 Created: 2012-03-19 Last updated: 2012-03-20Bibliographically 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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Schelin, LinaSjöstedt-de Luna, Sara

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CiteExportLink to record
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Citation style
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