Article1988

Estimation and Model Identification for Continuous Spatial Processes

537 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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Spatial and Panel Data Analysis Soil Geostatistics and Mapping Gaussian Processes and Bayesian Inference

Abstract

SUMMARY Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately described by a linear model with residuals that follow a second-order stationary Gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations. A general class of two-dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function. An iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non-lattice data. The procedure is applied to several generated data sets and to an actual ground-water data set.

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References

1981Spatial statistics 1983Spatial Processes, Models and Applications 1981Spatial Statistics 1975Statistical Analysis of Non-Lattice Data 1982Spatial Processes: Models and Applications 1985Fitting variogram models by weighted least squares 1984Maximum Likelihood Estimation of Models for Residual Covariance in Spatial Regression

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