Determining Spatial Correlation Structure Using a Flexible Method

ABSTRACT Modelling spatial data using geostatistical methods relies on parametric variograms and covariances. Ordinary, weighted and generalized least square, maximum and restricted maximum likelihood are some methods to estimate spatial processes' variogram (covariogram) parameters. Nevertheless, these methods necessarily do not result in the best prediction values for each desired loss function. This paper introduced a new method to estimate and optimize parameters of the spatial variogram and covariance functions based on a desired loss function to achieve cross‐validated prediction results. The proposed method can be used for different kriging techniques to perform the best prediction values and some desired loss functions such as mean, mean square and mean absolute error and complicated loss function like Linex conveniently. The variogram parameters were estimated under optional desired criteria to control how much they overestimate or underestimate observations. This feature can apply a wide range of controlled conditions to the model. The results indicated the interesting advantages of the suggested workflow versus previous variogram estimation methods. This method provides the best directional variogram, which enhances cross‐validation results when used with generalized least squares as an optimal estimation method for statistical efficiency.