Spatial regression models using inter-region distances in a non-random context.

摘要

In this thesis we deal with spatial data obtained at a single time. Spatial data can be encountered in many disciplines such as mining, agriculture, atmospheric science, ecology, epidemiology, hydrology, meteorology, waste disposal, and so on. Often the goal of such a study is a prediction at an unsampled location.; Let Z = (Z(s1), Z(s2), ..., Z( sn))' be the vector of the observed values at locations s1, s 2, ..., sn. The objective is to predict the unobserved value Z(s0) at location s0 which is not one of s 1, s2, ..., sn.; In this thesis we introduce a new method to predict spatial data. We assume that data come from a signal plus error model. In addition we assume the existence of hot spots locations with high activity, meaning that high values occur at or near them. As we move from these hot spots the values tend to decay. We assume an exponential decaying function, whose decay parameter has to be estimated.; Unlike kriging, we do not use the spatial correlation explicitly. Kriging assumes a random field expressed through the variogram and thus variation is in the error term. We assume simple uncorrelated errors and a more complicated, interesting signal. The spatial correlation that appears to be present in spatial data may be due to the signal. Once this signal is identified, and we assume that it is due to hot spots, then what is left is a white noise.; We first have to correctly identify the locations of the hot spots, estimate the decay parameter, and test whether a hot spot indeed exists. We then compare the proposed method to kriging through simulations and real data. In simulations, data are generated using our model and using the model assumed by kriging. When data are generated using our model, the new proposed method is a big winner, whereas when using the kriging model, the proposed method challenges kriging. In the two real data sets used here, the proposed method outperforms kriging.; We conclude that the proposed method can perform very well if the hot spots are present. Further, we believe that the hot spot model is realistic for a great many data sets.