| Spatial statistics has been applied widely to the fields of astronomy, agriculture, economics, biology, geography, geology, image processing, or any discipline that deals with data collected from different spatial locations. For example, in agriculture field, crop yield, measured at spatial locations, is assumed to vary linearly with different types of fertilizers. Spatial regression models play a very important role in assessing the effects with which we are concerned.; Statistics, from all its respects, relies on more or less stochastic models (or stochastic processes). A stochastic process is a collection of random variables {lcub}Z(t){rcub}, indexed by a set T. The general spatial model is based on such stochastic process, called random field, with the index set built on two or more dimensions. In statistical analysis, independence is a convenient assumption. However, such assumption is not realistic in the practical world. The correlated structures in two or more dimensional spaces are not simple extensions of the one-dimensional case, which makes the study of spatial regression in high dimensions both interesting and challenging. In the linear regression model, there exists wide-spread use of the LSE (least squares estimator), which has the property of “best unbiased estimator” under normality and “best linear unbiased estimator” without normal assumption. In this thesis, a linear spatial regression model is constructed based on correlated errors, which are assumed to follow either planar linear processes, or some mixing conditions. Under mild assumptions, the asymptotic normality of the least squares estimators is obtained for the above error structures by using either the Lyapounov condition or the Lindeberg condition. A blocking technique is used in the mixing case. The asymptotic property is employed to establish confidence intervals and simulation studies are done to evaluate the asymptotic normality under the planar linear process condition. |
