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September, 1993 Maximum Likelihood Estimation of Parameters under a Spatial Sampling Scheme
Zhiliang Ying
Ann. Statist. 21(3): 1567-1590 (September, 1993). DOI: 10.1214/aos/1176349272


We study in detail asymptotic properties of maximum likelihood estimators of parameters when observations are taken from a two-dimensional Gaussian random field with a multiplicative Ornstein-Uhlenbeck covariance function. Under the complete lattice sampling plan, it is shown that the maximum likelihood estimators are strongly consistent and asymptotically normal. The asymptotic normality here is normalized by the fourth root of the sample size and is obtained through higher order expansions of the likelihood score equations. Extensions of these results to higher-dimensional processes are also obtained, showing that the convergence rate becomes better as the dimension gets higher.


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Zhiliang Ying. "Maximum Likelihood Estimation of Parameters under a Spatial Sampling Scheme." Ann. Statist. 21 (3) 1567 - 1590, September, 1993.


Published: September, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0797.62019
MathSciNet: MR1241279
Digital Object Identifier: 10.1214/aos/1176349272

Primary: 62F12
Secondary: 60G15, 60G60

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 3 • September, 1993
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