Actual error rates in linear discrimination of spatial Gaussian data in terms of semivariograms

Abstract

The novel approach for classifying spatial Gaussian data based on Bayes discriminant functions in terms of semivariograms has been developed. We derived the closed-form expressions for the Maximum Likelihood estimator of regression parameters and the actual error rate (AER). Results are illustrated through simulation study of spatial Gaussian data sampled on a regular two-dimensional unit spacing lattice endowed with neighborhood structure based on Euclidean distance between sites. The accuracy of the derived AER for various values of spatial dependence parameters, Mahalanobis distances and neighborhood sizes are evaluated and compared.