Asymptotic Expansions for Correct Classification Rates in Discriminant Analysis

Asymptotic Expansions for Correct Classification Rates in Discriminant Analysis

When classifying an observation into one of k multivariate normal distributions based on samples of correctly classified observations, two estimates of the probability of correct classification, called the apparent and plug-in correct classification rates, are considered. Asymptotic expansions are f...

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Veröffentlicht in:The Annals of Statistics. - Institute of Mathematical Statistics. - 9(1981), 5, Seite 1002-1009
1. Verfasser: Schervish, Mark J. (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1981
Zugriff auf das übergeordnete Werk:The Annals of Statistics
Schlagworte:Classification error rates plug in error rate apparent error rate Mathematics Behavioral sciences Social sciences
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520 |a When classifying an observation into one of k multivariate normal distributions based on samples of correctly classified observations, two estimates of the probability of correct classification, called the apparent and plug-in correct classification rates, are considered. Asymptotic expansions are found for the means and variances of these estimates. It is shown that these expansions can be used to help reduce the bias of the estimates. In the course of finding the expansions, an asymptotic expansion for the conditional joint density of two observations given the sample mean and pooled covariance matrix is found. 
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