Date of Award
Doctor of Philosophy
Noel A. C. Cressie
Spatial statistics considers problems where the location of the data, as well as the data themselves, are thought to be important components of their statistical study. In particular, correlation between random variables at nearby locations might be used to improve inference techniques. This gives rise to a wide variety of difficult but fascinating statistical problems. This dissertation considers spatial statistical inference in the areas of estimation, hypothesis testing, and prediction;In the first section, a fundamental relationship between prediction and estimation is exploited to obtain biased predictors with smaller risk than the usual best linear unbiased (kriging) predictor. Assuming a general covariance structure, several such predictors are derived and their properties are discussed. Simultaneous multiple prediction is emphasized, and applications to spatial statistics are featured;In the second section, methods of inference using correlated data (with emphasis on testing equality of means in a one-way analysis of variance) are summarized and compared, and the consequences of overlooked spatial correlation are illustrated. The idea of a spatial analysis of variance is used to exploit intra-treatment correlation in order to obtain valid tests of significance.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Carol Anne Gotway
Gotway, Carol Anne, "Inference from spatial processes " (1989). Retrospective Theses and Dissertations. 9041.