Approximation of the expected error rate in classification of the Gaussian random field observations

The problem of classification of Gaussian random field observations into one of two populations specified by different regression mean models and common stationary covariance function is considered. The observations to be classified are assumed to be dependent on training sample. This is a more realistic assumption than the assumption of independence exploited in the previous papers. Unknown means parameters and common variance as a scale parameter are estimated from training sample. These estimators are plugged in the Bayes discriminant function. The approximation of the expected error rate associated with plug-in Bayes discriminant function is derived. This is the generalization of the known approximation. Numerical analysis of the accuracy of the proposed approximation in the small training sample case with locally optimal design is carried out.