Prediction by Regression and kriging for Spatial Data with Application

Abstract

This study deals with the prediction of the non-stationary spatial stochastic process. The prediction is done by two techniques which are regression technique (generalized least square estimation) and universal kriging technique. As it is familiar, that the non-stationary stochastic process has a trend (mean) as a linear or non-linear model. By this process we can find covariance function from knowing the variogram function and the latter is attributed to a spherical variogram model, also in order to estimate parameters of spherical model by minimum norm quadratic unbiased estimator which requires that the covariance function must be linear in the parameters, then changing the spherical model into an approximated linear model by Taylor series in the linear approximation The prediction in these two techniques is applied to real data which represent height levels of ground water of 47 wells with their regional coordinates in Sinjar district in Ninevah Governorate in Iraq. The results were so encouraging where we show the approximation between the predictive values and the real values as well as computing the variance of prediction in these two techniques. It is shown that the prediction variance of universal kringing is less than that of regression.