Expected error rate in linear discrimination of balanced spatial Gaussian time series

Abstract

The problems of discriminant analysis of spatial-temporal correlated Gaussian data were intensively considered previously (see e.g. Saltyte-Benth and Ducinskas (2005)). However, theoretical results were derived under the assumption of statistical independence between observation to be classified and training sample. In the present paper, we avoid this tough restriction. The problem of supervised classifying of the spatial Gaussian time series (SGTS) observation into one of two populations, is specified by different regression mean models and by common covariance function, is considered. In the case of complete parametric certainty and with the fixed training sample locations, the formula of conditional Bayes error rate is derived. In the case of unknown regression parameters and temporal covariance matrix, their ML estimators are plugged into the Bayes discriminant function. The asymptotic approximation of expected error rate is derived. This result is multivariate generalization of previous ones