Open Access
February 2014 Asymptotic theory of cepstral random fields
Tucker S. McElroy, Scott H. Holan
Ann. Statist. 42(1): 64-86 (February 2014). DOI: 10.1214/13-AOS1180


Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the autocovariance matrix. We also provide a comprehensive treatment of the asymptotic theory for two-dimensional random field models: we establish asymptotic results for Bayesian, maximum likelihood and quasi-maximum likelihood estimation of random field parameters and regression parameters. The theoretical results are presented generally and are of independent interest, pertaining to a wide class of random field models. The results for the cepstral model facilitate model-building: because the cepstral coefficients are unconstrained in practice, numerical optimization is greatly simplified, and we are always guaranteed a positive definite covariance matrix. We show that inference for individual coefficients is possible, and one can refine models in a disciplined manner. Our results are illustrated through simulation and the analysis of straw yield data in an agricultural field experiment.


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Tucker S. McElroy. Scott H. Holan. "Asymptotic theory of cepstral random fields." Ann. Statist. 42 (1) 64 - 86, February 2014.


Published: February 2014
First available in Project Euclid: 15 January 2014

zbMATH: 1294.62044
MathSciNet: MR3161461
Digital Object Identifier: 10.1214/13-AOS1180

Primary: 62F12 , 62M30
Secondary: 62F15 , 62M10

Keywords: Bayesian estimation , cepstrum , exponential spectral representation , Lattice data , spatial statistics , Spectral density

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • February 2014
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