Performance Evaluations of Gaussian Spatial Data Classifiers Based on Hybrid Actual Error Rate Estimators

Abstract

Discrimination and classification of spatial data has been widely mentioned in the scientific literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by introducing the method of statistical classification based on Bayes discriminant function (BDF) and by providing original approach for the classifier performance evaluation. Supervised classification of spatial data with response variable modelled by Gaussian random fields (GRF) with continuous or discrete spatial index is studied. Populations are assumed to be with different regression parameters vectors. Classification rule based on BDF with inserted ML estimators of regression and scale parameters is studied. We focus on the derived actual error rate (AER) and the approximation of the expected error rate (AEER) for both types of models. These are used in the construction of hybrid actual error rate estimators that are spatial modifications of widely applicable D and O estimators applied in cases of independent observations.

Simulation experiments are used for comparison of proposed AER estimators by the minimum of unconditional mean squared error criterion for both types of GRF models.