The Annals of Statistics

Estimating deformations of isotropic Gaussian random fields on the plane

Ethan B. Anderes and Michael L. Stein

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This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on ℝ2 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.

Article information

Ann. Statist., Volume 36, Number 2 (2008), 719-741.

First available in Project Euclid: 13 March 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M30: Spatial processes 62M40: Random fields; image analysis
Secondary: 60G60: Random fields

Deformation quasiconformal maps nonstationary random fields


Anderes, Ethan B.; Stein, Michael L. Estimating deformations of isotropic Gaussian random fields on the plane. Ann. Statist. 36 (2008), no. 2, 719--741. doi:10.1214/009053607000000893.

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