| Many disciplines (e.g., geology, soil science, image processing, epidemiology, crop science, ecology, forestry, astronomy) work with data collected from different spatial locations. This gives interest to investigating spatial correlations that may exist among the data. Throughout this dissertation, spatial correlation is modeled through the variogram.; The Weighted Least Squares estimator is widely used in geostatistics to estimate variogram parameters. It involves fitting a non-linear variogram model to the method of moments estimator for the variogram. However, the asymptotic properties of the Weighted Least Squares estimator have yet to be investigated. In Chapter 2, Weighted Least Squares estimators are demonstrated to be n -consistent and asymptotically normally distributed under some mild regularity conditions in the general linear geostatistical model.; Geostatistical data frequently involves counts or proportions, where general linear geostatistical modeling may not be appropriate. The generalized linear model is considered in Chapter 3 for modeling these types of data. An algorithm combining Generalized Estimating Equations and Weighted Least Squares is developed for estimating the mean and the variogram parameters. The estimators derived from the proposed estimating algorithm are shown to be n -consistent.; In Chapter 4, the parameter estimation methodology described in Chapter 3 is applied to the North American Breeding Bird Survey data, in which both the mean and spatial correlation of red-winged blackbird counts are estimated. Spatial prediction at unsampled sites is also carried out using Gotway and Stroup's (1997) simple kriging method. |
