The Annals of Statistics

Maximum Likelihood Estimation of Parameters under a Spatial Sampling Scheme

Zhiliang Ying

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Abstract

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.

Article information

Source
Ann. Statist., Volume 21, Number 3 (1993), 1567-1590.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349272

Digital Object Identifier
doi:10.1214/aos/1176349272

Mathematical Reviews number (MathSciNet)
MR1241279

Zentralblatt MATH identifier
0797.62019

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 60G60: Random fields 60G15: Gaussian processes

Keywords
Gaussian random fields multiplicative covariance functions lattice sampling maximum likelihood estimation computer experiments consistency asymptotic normality

Citation

Ying, Zhiliang. Maximum Likelihood Estimation of Parameters under a Spatial Sampling Scheme. Ann. Statist. 21 (1993), no. 3, 1567--1590. doi:10.1214/aos/1176349272. https://projecteuclid.org/euclid.aos/1176349272


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