Abstract

In this paper the problem of classification of an observation into one of two Gaussian populations with different means and common variance is considered in the case when equicorrelated training sample is given. Unknown means and common variance are estimated from training sample and these estimators are pluged in the Bayes discriminant function. The maximum likelihood estimators are used. The approximation of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of that approximation for various values of correlation is presented.

Highlights

  • Discriminant analysis (DA) sometimes called supervised classification traditionally assumes that observations to be classified and observations in training sample are independent

  • We consider the performance of the plug-in linear Bayes discriminant function (PBDF) when the parameters are estimated from training samples as realizations of a equicorrelated Gaussian random process

  • We use the maximum likelihood (ML) estimators of unknown parameters of means and common variance assuming that the correlation is known

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Summary

Introduction

Discriminant analysis (DA) sometimes called supervised classification traditionally assumes that observations to be classified and observations in training sample are independent. In practical situations with temporally and spatially distributed data this is usually not the case. Data that are close together in time or space, are likely to be correlated, at best equicorrelated [4, 5]. To include temporal or spatial dependencies in the classification problem is very important. We consider the performance of the plug-in linear Bayes discriminant function (PBDF) when the parameters are estimated from training samples as realizations of a equicorrelated Gaussian random process. We use the maximum likelihood (ML) estimators of unknown parameters of means and common variance assuming that the correlation is known

The main concepts and definitions
The proposed approximation
Numerical illustration and discussions
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