Regularized kriging as a generalization of simple, universal, and bayesian kriging

In this article the properties of regularized kriging (RK) are studied. RK is obtained as a result of relaxing the universal kriging (UK) non-bias condition by using the support vectors methodology. More specifically, we demonstrate how RK is a continuum of solutions in function of the regularizing parameter, which includes as particular and extreme cases, simple kriging (SK) and UK, and as an intermediate case, Bayesian kriging (BK). Likewise, expressions are obtained for the mean, variance and mean squared error (MSE), as also the expression for the corresponding estimator of the coefficients of the mean. Finally, we investigate the relationship between RK and the support vector machines. By means of simulations we compare the MSE for RK with those for BK and UK, for different association models, for different levels of noise, and for differently sized mean coefficients. The RK results prove to be an improvement on the UK and BK results, and, moreover, these improvements are proportionally greater for greater levels of noise.