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Gaussian maximum likelihood estimation for ARMA models II: spatial processes

Yao, Qiwei ORCID: 0000-0003-2065-8486 and Brockwell, Peter J (2006) Gaussian maximum likelihood estimation for ARMA models II: spatial processes. Bernoulli, 12 (4). pp. 403-429. ISSN 1350-7265

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Identification Number: 10.3150/bj/1151525128


This paper examines the Gaussian maximum likelihood estimator (GMLE) in the context of a general form of spatial autoregressive and moving average (ARMA) processes with finite second moment. The ARMA processes are supposed to be causal and invertible under the half-plane unilateral order, but not necessarily Gaussian. We show that the GMLE is consistent. Subject to a modification to confine the edge effect, it is also asymptotically distribution-free in the sense that the limit distribution is normal, unbiased and has variance depending only on the autocorrelation function. This is an analogue of Hannan's classic result for time series in the context of spatial processes.

Item Type: Article
Official URL:
Additional Information: © 2006 Bernoulli Society for Mathematical Statistics and Probability
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 05 Jun 2008 14:00
Last Modified: 20 Oct 2021 03:12
Projects: DMS0308109
Funders: Leverhulme Trust, National Science Foundation

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