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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Abstract

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

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

Dates
First available in Project Euclid: 13 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1205420517

Digital Object Identifier
doi:10.1214/009053607000000893

Mathematical Reviews number (MathSciNet)
MR2396813

Zentralblatt MATH identifier
1133.62077

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

Keywords
Deformation quasiconformal maps nonstationary random fields

Citation

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. https://projecteuclid.org/euclid.aos/1205420517


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