Analysis of non-stationary spatial data : A study on the performances of Universal Kriging, Median-Polish Kriging and LOESS

One of major problems in spatial analysis is to estimate the value z(s(0)) at an unknown location s(0) using the information about observations z(s(α)), α = 1,…,n. In this article, we will perform a numerical study about some methods for this problem. That is, we examine both the tranditional statistical method which does not take into account spatial correlation and the spatial statistical method which takes into account spatial correlation by applying them to a set of non-stationary spatial data. We compare the predictive powers of these methods. More precisely, we choose Universal Kriging(UK) and Median-Polish Kriging(MPK) as spatial statistical methods, and locally weighted regression or LOESS as a traditional method. As the major criterion for comparison, we use the so-called PRESS statistic, and also draw the prediction surface plot and the prediction standard error surface plot as minor criteria. A real numerical example of non-stantionary spatial data is analyzed for the comparison among the above three methods.