论文信息 - Estimating Nonstationary Spatial Correlations

Estimating Nonstationary Spatial Correlations

The paper is concerned with the estimation of a spatial correlation structure under circumstances when the usual assumptions of stationarity and isotropy do not apply. An ingenious approach due to Sampson and Guttorp is based on a nonlinear transformation of the sampling space into an alternative space within which the spatial structure is stationary and isotropic. However the actual algorithm devised by Sampson and Guttorp is complicated and has a number of ad hoc features. In this paper we consider alternative methods based on parametric maximum likelihood ts, using a radial basis function representation of the nonlinear map. A key part of the tting procedure is model selection, or equivalently, reduction in dimensionality by selection of a subset of radial basis functions. The methodology is illustrated with two examples, one based on tropospheric ozone and the other on U.S. climate data. However a number of cautions are noted: there is no guarantee of uniqueness of the estimates and the evidence that more complicated models result in improved spatial predictions is, at best, inconclusive.

Richard J. Smith | Richard J. Smith

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