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Biometrika 1982 69(1):95-105; doi:10.1093/biomet/69.1.95
© 1982 by Biometrika Trust
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Parameter estimation for a stationary process on a d-dimensional lattice

XAVIER GUYON

Laboratoire de Statistique, Université Paris XI Orsay, France

We study asymptotic properties of various estimation procedures for a general stationary regular process on a d-dimensional lattice. Differences between d = 1, time series, and d ≥ 2 spatial processes, are pointed out. We suppose that the process is observed on a set PN, with cN points, which tends to infinity with the same speed in all directions. The relative edge effect is of order cN–1/d, increasing with d: this effect is without statistical importance if d = 1, but is important if d ≥ 2. We give a {surd}cN-consistent, asymptotically normal estimator of the underlying parameter, the procedure being constructed by a modification of Whittle's approximation to the log likelihood. In the Gaussian case, this procedure is asymptotically efficient.

Key Words: Consistency • Edge effect • Log likelihood approximation • Spectral density • Stationary regular process


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