Mathematics – Statistics Theory
Scientific paper
2011-12-08
Mathematics
Statistics Theory
27 pages
Scientific paper
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. Given the importance of this topic, there has been substantial research devoted to this area. However, in spite of the tremendous research to date, outside the engineering literature, the cepstral random field model remains largely underdeveloped. We provide a comprehensive treatment of the asymptotic theory for cepstral random field models. In particular, we provide recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the necessary autocovariance matrix. Additionally, we establish asymptotic consistency results for Bayesian, maximum likelihood, and quasi-maximum likelihood estimation. Further, in both the maximum and quasi-maximum likelihood frameworks we derive the asymptotic distribution of our estimator. The theoretical results are presented generally and are of independent interest, pertaining to models outside the cepstral random field setting. Finally, we argue that the cepstral representation is advantageous from a modeling perspective. More specifically, the cepstral coefficients have an unrestricted parameter space and, thus, the resulting estimated covariance matrix is guaranteed to remain positive definite.
Holan Scott H.
McElroy Tucker S.
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