More Efficient Prediction for Ordinary Kriging to Solve a Problem in the Structure of Some Random Fields

Abstract

Recently, some specific random fields have been defined based on multivariate distributions. This paper will show that almost all these random fields have a deficiency in spatial autocorrelation structure. The paper recommends a method for coping with this problem. Another application of these random fields is spatial data prediction, and the Kriging estimator is the most widely used method that does not require defining the mentioned random fields. Although it is an unbiased estimator with a minimum mean-squared error, it does not necessarily have a minimum mean-squared error in the class of all linear estimators. In this work, a biased estimator is introduced with less mean-squared error than the Kriging estimator under some conditions. Asymptotic behavior of its basic component will be investigated too.