Estimation in random field models for noisy spatial data

Abstract

The random field model has been applied to model spatial heterogeneity for spatial data in many applications. The purpose of this dissertation is to explore statistical properties of noisy spatial data through estimation of the Gaussian random field. Large sample properties of the Maximum Likelihood Estimator (MLE) of an Onrstein-Uhlenbeck process model with measurement error are studied. The effect caused by adding measurement error, or "nugget," is revealed by the fixed region asymptotics of the MLE. The kriging predictor with estimated covariance is discussed under such models. An extension to regression models is proposed and its asymptotic properties are examined.

The Gaussian random field is characterized by its corresponding covariance function. By means of constructing the multi-dimensional covariance function from one-dimensional covariance functions, some spatial process models applicable to both spatial and regression data are proposed. The estimation of covariance functions for these models is studied. Large sample theory for some estimators is provided.