CONSISTENT ESTIMATES OF DEFORMED ISOTROPIC GAUSSIAN RANDOM FIELDS ON THE PLANE

• 成果类型: Article
• 署名作者: Anderes, Ethan; Chatterjee, Sourav
• 署名单位: University of California System; University of California Davis; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS647
• 发表日期: 2009
• 页码: 2324-2350
• 关键词: estimating deformations; QUADRATIC VARIATION; identification; texture; version; shape

摘要

This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f:R-2 -> R-2 when observint, the deformed oil a dense,rid in a bounded, simply connected random field Z o f on a dense grid in a bounded, simply connected domain Omega, where Z is assumed to be an isotropic Gaussian random field on R-2. The estimate f is constructed on a simply connected domain U, such that (U) over bar subset of Omega and is defined using kernel smoothed quadratic variations, Bergman projections and results from quasi con formal theory. We show, under mild assumptions oil the random field Z and the deformation f, that (f) over cap -> R-theta f + c uniformly oil compact subsets of U with probability one as the grid spacing goes to zero. where R-theta is an unidentifiable rotation and c is all unidentifiable translation.