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Spatial prediction in the presence of left-censoring
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.
2014 (English)In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 74, 125-141 p.Article in journal (Other academic) Published
Abstract [en]

Environmental (spatial) monitoring of different variables often involves left-censored observations falling below the minimum detection limit (MDL) of the instruments used to quantify them. Several methods to predict the variables at new locations given left-censored observations of a stationary spatial process are compared. The methods use versions of kriging predictors, being the best linear unbiased predictors minimizing the mean squared prediction errors. A semi-naive method that determines imputed values at censored locations in an iterative algorithm together with variogram estimation is proposed. It is compared with a computationally intensive method relying on Gaussian assumptions, as well as with two distribution-free methods that impute the MDL or MDL divided by two at the locations with censored values. Their predictive performance is compared in a simulation study for both Gaussian and non-Gaussian processes and discussed in relation to the complexity of the methods from a user’s perspective. The method relying on Gaussian assumptions performs, as expected, best not only for Gaussian processes, but also for other processes with symmetric marginal distributions. Some of the (semi-)naive methods also work well for these cases. For processes with skewed marginal distributions (semi-)naive methods work better. The main differences in predictive performance arise for small true values. For large true values no difference between methods is apparent.

Place, publisher, year, edition, pages
Elsevier, 2014. Vol. 74, 125-141 p.
Keyword [en]
kriging, left-censoring, minimum detection limit, prediction, spatial process
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-53278DOI: 10.1016/j.csda.2014.01.004ISI: 000333781500010OAI: oai:DiVA.org:umu-53278DiVA: diva2:511108
Note

Originally published in dissertation in manuscript form.

Available from: 2012-03-20 Created: 2012-03-19 Last updated: 2017-12-07Bibliographically 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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