Academic

PhD Oral Presentation:

This thesis focus on 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 sampling design and randomized sampling design, 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 two microergodic parameters (including the smoothness 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. Besides, it is also proved that some parameters cannot be consistently estimated.