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Biometrika 1987 74(3):517-524; doi:10.1093/biomet/74.3.517
© 1987 by Biometrika Trust
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Intrinsic autoregressions and related models on the two-dimensional lattice

HANS R. KÜNSCH

Eidgenössische Technische Hochschule, Seminar für Statistik, 8092 Zürich, Switzerland

Stationary autoregressions on a two-dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary. Prediction formulae and the asymptotic behaviour of the semivariogram are derived. For parameter estimation we propose an approximate maximum likelihood estimator, a generalization of Whittle's estimator; it is derived also for general intrinsic models.

Key Words: Approximate maximum likelihood • Autoregression on Z2 • Intrinsic model • Mean free prediction • Semivariogram


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