Expected Error Rate in Classification of the Gaussian Random Field Observation

Abstract

The problem of classification of Gaussian random field observations into one of two populations specified by different regression mean models and common stationary covariance with unknown scale parameter is considered. Unknown parameters are estimated from training sample and these estimators are plugged in the Bayes discriminant function. The asymptotic expansion of the expected error rate associated with Bayes plug - in discriminant function is derived. Numerical analysis of the accuracy of approximation based on derived asymptotic expansion in the small training sample case is carried out.