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Sampling designs and prediction methods for Gaussian spatial processes. (English) Zbl 0941.62104
Ghosh, Subir (ed.), Multivariate analysis, design of experiments, and survey sampling. A tribute to Jagdish N. Srivastava. New York, NY: Marcel Dekker. Stat., Textb. Monogr. 159, 1-54 (1999).
Introduction: For a phenomenon that varies over a continuous (or even a large finite) spatial domain, it is seldom feasible, or even possible, to observe every potential datum of some study variable associated with that phenomenon. Thus, an important part of statistics is statistical sampling theory, where inference about the study variable may be made from a subset, or sample, of the potential data.
Spatial sampling refers to the sampling of georeferenced or spatially labeled phenomena. In the spatial context, interest is usually in the prediction of (some function of) the study variable at multiple unsampled sites, and it is in this sense that the prediction problem is multivariate. Given some predictand together with its predictor, a best sampling plan or network refers to the choice of locations at which to sample the phenomenon in order to achieve optimality according to a given criterion (e.g., minimize average mean squared prediction error, where the average is taken over multiple prediction locations). In practice, optimal sampling plans may be extremely difficult to achieve, but good, although suboptimal, sampling plans may be relatively easy to obtain and these designs, at least, should be sought. A commonly chosen predictand in survey sampling is the total (or mean) of the study variable over a specified spatial domain. In this article, we shall also consider predictands defined over some “local” subregion of the domain, and predictands that are nonlinear functions of the study variable at multiple spatial locations.
The objective of this paper is to gauge, through a carefully designed simulation experiment, the performance of different prediction methods under different sampling designs, over several realizations of a spatial process whose strength of spatial dependence varies from zero to very strong. Included are both “spatial” and “nonspatial” analyses and designs. Our emphasis is on prediction of spatial statistics defined on both “local” and “global” regions, based on data obtained from a global network of sampling sites. A brief review of geostatistical theory, survey-sampling theory, and of the spatial-sampling literature is given in Section 2. Based on this knowledge, we designed a simulation experiment whose details are described in Section 3. Section 4 analyzes the results of the experiment and conclusions are given in Section 5.
For the entire collection see [Zbl 0927.00053].

##### MSC:
 62M30 Inference from spatial processes 62D05 Sampling theory, sample surveys 65C60 Computational problems in statistics (MSC2010)
##### Keywords:
prediction; spatial-sampling; simulation