Comparison of maximum likelihood and ordinary least squares estimators in discriminant analysis of equicorrelated gaussian observations

Author:

Kęstutis DUČINSKAS

AMS Classification:

62H30, 62H12, 62M40

Keywords:

actual error rate, Bayes discriminant function, expected error rate, equicorrelation

Abstract:

In this paper, the problem of classification of an observation into one of two Gaussian populations is considered. The observation to be classified is assumed to be equicorrelated with each observation in the training sample consisting of univariate equicorrelated observations. Unknown means and common variance are estimated from training sample, and these estimators are pluged in the Bayes Discriminant Function (BDF) formed by the ratio of conditional densities. For the estimation of unknown parameters, two methods, namely, maximum likelihood and ordinary least squares are used. The approximations of the expected error rate associated with plug-in BDF function are derived. These are the generalizations of expected error rate approximations derived previously under different rarely realistic assumptions of independence. Numerical analysis of the accuracy of those approximations for different estimators is presented.

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Ducinskas-09.pdf

Vol. 4 (12), 2009