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COVARIANCE MODELS FOR LATTICE DATA
Authors:H. T. Kiivefu   N. A. Campbell
Affiliation:Division of Mathematics and Statistics, CSIRO Wembley 6014, Western Australia
Abstract:Given observations on an m × n lattice, approximate maximum likelihood estimates are derived for a family of models including direct covariance, spatial moving average, conditional autoregressive and simultaneous autoregressive models. The approach involves expressing the (approximate) covariance matrix of the observed variables in terms of a linear combination of neighbour relationship matrices, raised to a power. The structure is such that the eigenvectors of the covariance matrix are independent of the parameters of interest. This result leads to a simple Fisher scoring type algorithm for estimating the parameters. The ideas are illustrated by fitting models to some remotely sensed data.
Keywords:Rectangular lattice    torus lattice    spatial correlation    direct covariance models    moving average    conditional autoregression    simultaneous autoregression    likelihood approximation    Fisher scoring algorithm
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