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Biometrika 1977 64(2):367-373; doi:10.1093/biomet/64.2.367
© 1977 by Biometrika Trust
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A spectral moment estimation problem in two dimensions

ROBERT J. ADLER

C.S.I.R.O. Division of Mathematics and Statistics Newton, N.S.W.

The estimation is considered, of a certain function of the second-order spectral moments of a Gaussian process whose ‘time’ parameter lies in the plane. Two types of estimate are considered, both based on the level crossings of the process. The first is applicable when the values of the process are recorded continuously over the plane, the second when the values are known only on a planar lattice. The consistency of both estimators is studied.

Key Words: Euler characteristic • Excursion set • Gaussian random field • Level crossing • Spectral moment


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