Consistent estimates of deformed isotropic Gaussian random fields on the plane
Ethan Anderes and Sourav Chatterjee
Source: Ann. Statist. Volume 37, Number 5A
(2009), 2324-2350.
Abstract
This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f: ℝ2→ℝ2 when observing the deformed random field Z○f 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 f̂ is constructed on a simply connected domain U, such that U̅⊂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 f̂→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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Permanent link to this document: http://projecteuclid.org/euclid.aos/1247663757
Digital Object Identifier: doi:10.1214/08-AOS647
Zentralblatt MATH identifier: 05596903
Mathematical Reviews number (MathSciNet): MR2543694
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