Estimating deformations of isotropic Gaussian random fields on the plane

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Anderes, Ethan B.
Stein, Michael L.
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Abstract
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This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package--from model assumptions to algorithmic recovery of the deformation--for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.
Comment: Published in at http://dx.doi.org/10.1214/009053607000000893 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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Mathematics - Statistics Theory, 62M30, 62M40 (Primary) 60G60 (Secondary)
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