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October 2009 Consistent estimates of deformed isotropic Gaussian random fields on the plane
Ethan Anderes, Sourav Chatterjee
Ann. Statist. 37(5A): 2324-2350 (October 2009). DOI: 10.1214/08-AOS647


This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f: ℝ2→ℝ2 when observing the deformed random field Zf on a dense grid in a bounded, simply connected domain Ω, where Z is assumed to be an isotropic Gaussian random field on ℝ2. The estimate is constructed on a simply connected domain U, such that ⊂Ω and is defined using kernel smoothed quadratic variations, Bergman projections and results from quasiconformal theory. We show, under mild assumptions on the random field Z and the deformation f, that Rθf+c uniformly on compact subsets of U with probability one as the grid spacing goes to zero, where Rθ is an unidentifiable rotation and c is an unidentifiable translation.


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Ethan Anderes. Sourav Chatterjee. "Consistent estimates of deformed isotropic Gaussian random fields on the plane." Ann. Statist. 37 (5A) 2324 - 2350, October 2009.


Published: October 2009
First available in Project Euclid: 15 July 2009

zbMATH: 1171.62056
MathSciNet: MR2543694
Digital Object Identifier: 10.1214/08-AOS647

Primary: 60G60, 62M30, 62M40
Secondary: 62G05

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 5A • October 2009
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