The Annals of Statistics

Fixed-domain asymptotic properties of tapered maximum likelihood estimators

Juan Du, Hao Zhang, and V. S. Mandrekar

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 6A (2009), 3330-3361.

Dates
First available in Project Euclid: 17 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1250515389

Digital Object Identifier
doi:10.1214/08-AOS676

Mathematical Reviews number (MathSciNet)
MR2549562

Zentralblatt MATH identifier
1369.62248

Subjects
Primary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 62G20: Asymptotic properties 60G15: Gaussian processes

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

Citation

Du, Juan; Zhang, Hao; Mandrekar, V. S. Fixed-domain asymptotic properties of tapered maximum likelihood estimators. Ann. Statist. 37 (2009), no. 6A, 3330--3361. doi:10.1214/08-AOS676. https://projecteuclid.org/euclid.aos/1250515389


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