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Biometrika 1987 74(4):877-882; doi:10.1093/biomet/74.4.877
© 1987 by Biometrika Trust
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MISCELLANEA

Edge effects and efficient parameter estimation for stationary random fields

R. DAHLHAUS and H. KÜNSCH

Universität Essen Fachbereich Mathematik, D-4300 Essen 1, Federal Republic of Germany
Seminar für Statistik ETH-Zentrum, CH-8092 Zurich, Switzerland

We consider the estimation of the parameters of a stationary random field on d-dimensional lattice by minimizing the classical Whittle approximation to the Gaussian log likelihood. If the usual biased sample covariances are used, the estimate is efficient only in one dimension. To remove this edge effect, we introduce data tapers and show that the resulting modified estimate is efficient also in two and three dimensions. This avoids the use of the unbiased sample covariances which are in general not positive-definite.

Key Words: Edge effect • Data taper • Sample covariance • Stationary random field • Strong mixing • Whittle function


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