Asymptotic Theory of Cepstral Random Fields
| dc.contributor.author | McElroy, T.S. | |
| dc.contributor.author | Holan, S.H. | |
| dc.date.accessioned | 2013-10-16T18:56:12Z | |
| dc.date.available | 2013-10-16T18:56:12Z | |
| dc.date.issued | 2013 | |
| dc.description | http://arxiv.org/pdf/1112.1977.pdf | en_US |
| dc.description.abstract | 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 a substantial amount of research devoted to this area. However, the cepstral random field model remains largely underdeveloped outside the engineering literature. We provide a comprehensive treatment of the asymptotic theory for two-dimensional 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 of random field parameters and regression parameters. 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 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. Finally, our results are illustrated through simulation and the analysis of straw yield data in an agricultural field experiment. | en_US |
| dc.description.sponsorship | NSF-NCRN | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/34461 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Annals of Statistics | en_US |
| dc.subject | Bayesian estimation | en_US |
| dc.subject | Cepstrum | en_US |
| dc.subject | Exponential spectral repr esentation | en_US |
| dc.subject | Lattice data | en_US |
| dc.subject | Spatial statistics | en_US |
| dc.subject | Spectral density | en_US |
| dc.title | Asymptotic Theory of Cepstral Random Fields | en_US |
| dc.type | preprint | en_US |
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