Modeling spatial covariance functions

Choi, InKyung Ph.D., Purdue University, December 2014. Modeling spatial covariance functions. Major Professor: Hao Zhang. Covariance modeling plays a key role in the spatial data analysis as it provides important information about the dependence structure of underlying processes and determines performance of spatial prediction. Various parametric models have been developed to accommodate the idiosyncratic features of a given dataset. However, the parametric models may impose unjustified restrictions to the covariance structure and the procedure of choosing a specific model is often ad-hoc. In the first part of the dissertation, a new nonparametric covariance model that can avoid the choice of parametric forms is proposed. The estimator is obtained via a nonparametric approximation of completely monotone functions. It is easy to implement and simulation study shows it outperforms the parametric models when there is no clear information on model specification. Two real datasets are analyzed to illustrate the proposed approach and provide further comparison between the nonparametric and parametric models. Most spatial covariance models assume that the dependence becomes stronger when two locations are closer to each other and thus assume that the dependence is negligible when two locations are far apart from one another. However long-distance connection can occur in climate variables through, for example, high altitude winds or large-scale atmospheric waves propagation. This phenomenon is called teleconnection and often considered to be responsible for extreme weather events occurring simultaneously around the world. In the second part of the dissertation, a nonstationary spatial covariance model for long-distance dependence is proposed. The model allows the spatial dependence to vary with time so that temporal dynamics of the telecon-