Open Access
December 2009 Fixed-domain asymptotic properties of tapered maximum likelihood estimators
Juan Du, Hao Zhang, V. S. Mandrekar
Ann. Statist. 37(6A): 3330-3361 (December 2009). DOI: 10.1214/08-AOS676


When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency of the maximum likelihood estimator (MLE) for the microergodic parameter in the Matérn covariance function by establishing the fixed-domain asymptotic distribution of the exact MLE and that of the tapered MLE. Our results imply that, under some conditions on the taper, the tapered MLE is asymptotically as efficient as the true MLE for the microergodic parameter in the Matérn model.


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Juan Du. Hao Zhang. V. S. Mandrekar. "Fixed-domain asymptotic properties of tapered maximum likelihood estimators." Ann. Statist. 37 (6A) 3330 - 3361, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1369.62248
MathSciNet: MR2549562
Digital Object Identifier: 10.1214/08-AOS676

Primary: 62M20
Secondary: 60G15 , 62G20

Keywords: covariance tapering , equivalence of measures , fixed-domain asymptotics , Matérn covariance functions , maximum likelihood estimator , spatial statistics

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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