Error Bounds for Asymptotic Approximations of the Linear Discriminant Function When the Sample Sizes and Dimensionality are Large

Theoretical accuracies are studied for asymtotic approximations of the expected probabilities of misclassification (EPMC) when the linear discriminant function is used to classify an observation as coming from one of two multivariate normal populations with a common covariance matrix. The asymptotic...

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Bibliographic Details
Published in:Journal of multivariate analysis 2000-04, Vol.73 (1), p.1-17
Main Author: Fujikoshi, Yasunori
Format: Article
Language:English
Subjects:
asymptotic approximations
asymptotic approximations, error bounds, expected probability of misclassification, linear discriminant function
Distribution theory
error bounds
Exact sciences and technology
expected probability of misclassification
linear discriminant function
Mathematics
Multivariate analysis
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:Theoretical accuracies are studied for asymtotic approximations of the expected probabilities of misclassification (EPMC) when the linear discriminant function is used to classify an observation as coming from one of two multivariate normal populations with a common covariance matrix. The asymptotic approximations considered are the ones under the situation where both the sample sizes and the demensionality are large. We give explicit error bounds for asymptotic approximations of EPMC, based on a general approximation result. We also discuss with a method of obtaining asymptotic expansions for EPMC and their error bounds.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.1999.1862