PARAMETER ESTIMATION FOR ISOTROPIC GAUSSIAN RANDOM FIELDS WITH GENERALIZED WENDLAND COVARIANCE FUNCTIONS FOR MATERN COVARIANCE FUNCTIONS WITH NUGGET

Abstract

We consider estimating the parameters for two of the most commonly used models in spatial statistics. The first one is the Gaussian random field (GRF) with isotropic generalized Wendland covariance functions, and the second one is the GRF having Matérn covariance functions with nugget. For the first model, the observed sites are taken via three different designs, namely a smooth curve, stratified and randomized sampling designs, while only the dataset observed via stratified sampling design is considered for the second model. For each set of observations, using higher-order quadratic variations, the estimators for the smoothness parameter, a microergodic parameter and the nugget parameter (for the second model only) are constructed. Under some mild conditions with all parameters are unknown, these estimators are shown to be consistent and the upper bounds to the convergence rates of them are also established with respect to the fixed domain asymptotics.