A1414
Title: Scalable covariance parameter estimation of nonstationary Matern process from high-resolution spatial data
Authors: Kunal Das - Iowa State University (United States) [presenting]
Zhengyuan Zhu - Iowa State University (United States)
Abstract: Accurately modeling nonstationary spatial dependence is crucial for high-resolution spatial data from satellite imaging and sensors. The aim is to tackle these challenges by estimating key parameters of nonstationary Gaussian random fields under infill asymptotics, explicitly focusing on the smoothness parameter and spatially varying microergodic functions within a Matern covariance framework. A divide-and-conquer strategy has been proposed utilizing recent advancements in higher-order quadratic variations with multivariate discrete differentiation. By overlaying a coarse grid of anchor points on the observation domain, locally stationary neighborhoods are constructed to estimate unknown but constant stationary parameters. Then, the spatially varying structure of the concerned parameters is obtained using kernel smoothing over the domain. The methodology provides theoretical guarantees for the asymptotic consistency of local and global estimators, without requiring prior knowledge of model parameters and under mild smoothness conditions of unknown component functions. This framework is scalable, interpretable, statistically robust, and relevant for geostatistical modeling applications. A two-fold simulation study is also discussed to assess the finite sample accuracy of asymptotic theoretical results and to illustrate the computational efficiency of the method compared to existing techniques for large spatial datasets.
