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Biometrika 1984 71(1):135-146; doi:10.1093/biomet/71.1.135
© 1984 by Biometrika Trust
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Maximum likelihood estimation of models for residual covariance in spatial regression

K. V. MARDIA and R. J. MARSHALL

Department of Statistics, University of Leeds U.K.

We describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters. Observations are assumed to be Gaussian. We give conditions which ensure consistency and asymptotic normality of the estimators. Our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators. We also discuss an application of the spectral approximation to the likelihood for processes on a lattice.

Key Words: Asymptotic normality • Consistency • Gaussian process • Kriging • Lattice process • Likelihood • Simulation • Spatial covariance


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