Hiroshima Mathematical Journal

An optimal discriminant rule in the class of linear and quadratic discriminant functions for large dimension and samples

Chieko Matsumoto

Full-text: Open access

Abstract

For the classification problem between two normal populations with a common covariance matrix, we consider a class of discriminant rules based on a general discriminant function $T$. The class includes the one based on Fisher’s linear discriminant function and the likelihood ratio rule. Our main purpose is to derive an optimal discriminant rule by using an asymptotic expansion of misclassification probability when both the dimension and the sample sizes are large. We also derive an asymptotically unbiased estimator of the misclassification probability of $T$ in our class.

Article information

Source
Hiroshima Math. J., Volume 34, Number 2 (2004), 231-250.

Dates
First available in Project Euclid: 22 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1150998164

Digital Object Identifier
doi:10.32917/hmj/1150998164

Mathematical Reviews number (MathSciNet)
MR2086844

Zentralblatt MATH identifier
1056.62078

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Citation

Matsumoto, Chieko. An optimal discriminant rule in the class of linear and quadratic discriminant functions for large dimension and samples. Hiroshima Math. J. 34 (2004), no. 2, 231--250. doi:10.32917/hmj/1150998164. https://projecteuclid.org/euclid.hmj/1150998164


Export citation