Abstract
The problem of classification of spatial Gaussian process observation into one of two populations specified by different regression mean models and common stationary covariance with unknown sill 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. Comparison of two spatial sampling designs based on values of this approximation is done.
Highlights
In classical discriminant analysis sometimes called supervised classification, the observations to be classified and observations in training sample are assumed to be independent
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
Summary
In classical discriminant analysis sometimes called supervised classification, the observations to be classified and observations in training sample are assumed to be independent. Saltyteand Ducinskas [5] derived the asymptotic expansion of the expected error rate when classifying the observation of a univariate Gaussian random field into one of two classes with different regression mean models and common variance. This result was generalized to multivariate spatial-temporal regression model in Saltyte-Benth and Ducinskas [6]. Performance of the plug-in linear discriminant function when the parameters are estimated from training sample formed by classified observations of Gaussian random field is analyzed. Similar problems for group spatial classification is considered in [7]
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