Title: Estimating Quasiconformal Deformations through Local Regression
Advisors: Prof. Tailen Hsing, Lec. Brian Thelen.
Committee Members: Assoc. Prof. Stilian Stoev
Abstract: Environmental processes are often nonstationary which makes spatial covariance estimation a difficult problem. This proposal explores various methods for modeling nonstationary, nonisotropic Gaussian processes and further develops the deformation approach by utilizing local regression. We assume that the nonstationary spatial process of interest, Y(t) is the deformation of an underlying istoropic Gaussian process, Z(t). Hence, Y(t)=Z(f(t)) , where f: R 2 R R 2 is the deformation function. Quasiconformal theory allows us to estimate this deformation function through estimating its Jacobian locally. We use local regression to estimate a function of the Jacobian, g(t), locally, when we observe a single realization of a deformed Gaussian random field on a dense grid, establishing infill assymptotic results on a fixed domain.