Abstract
The problem of discriminating between two n-variate normal populations with known but unequal means and covariance matrices is considered. Discrimination procedures are usually based on a statistic known as the discriminant function, whose probability distribution is needed to determine probabilities of misclassification. General distributional properties for the discriminant function associated with the Bayes procedure for this problem are discussed. Two new classes of discriminant functions are defined and developed. The first is the class of all statistics resulting from one-dimensional linear transformations of the observation vector. The second class results from those procedures based on independent transformed variates considered individually, where the Bayes procedure is applied to each. Optimal procedures for these classes are found and their probabilities of misclassification are spelled out. The methods are illustrated by a discriminant analysis of the eel populations s. brevidor salis and s. oregoni.
Zeis, Charles David (1972). Discrimination between normal populations with dissimilar covariance structure. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -187496.