A1769
Title: Parameter estimation for Matern random fields from local measurements
Authors: Randolf Altmeyer - Imperial College London (United Kingdom) [presenting]
Abstract: Gaussian random fields with Matern covariance structure are fundamental models in spatial statistics. Given discrete observations on a regular grid, parametric estimation of key parameters governing variance, range, and smoothness is studied. The approach is based on the representation of the random field as the solution to an elliptic stochastic partial differential equation (SPDE). A key insight from this representation is that the model parameters exhibit distinct local scaling behaviour, reflecting the local structure of the underlying differential operator. Building on this idea, spatially localised linear combinations of the data, referred to as local measurements, are constructed to approximate localised features of the field. By analysing how these quantities scale across resolutions, a novel class of estimators based on localised quadratic functionals is developed. This can be viewed as a multidimensional extension of quadratic variation techniques from time series analysis. By carefully designing test functions with prescribed moment cancellation properties, explicit estimators for the variance, range, and smoothness parameters are obtained. Asymptotic normality is established under infill and large domain asymptotics, and explicit expressions for the estimator variances are derived using Gaussian moment identities. The resulting methods are computationally efficient, with linear complexity in the number of observations.
