THE GENERALIZED DISCRIMINANT FUNCTION AND NUISANCE PARAMETERS IN CLASSIFICATION PROCEDURES.
Abstract
Extensions of the Fisher discriminant function have been given by several authors and S. N. Roy has generalized Fisher's approach to provide a generalized discriminant function applicable to the general multivariate linear mode. The paper considers the use of this discriminant function for classifying an individual into two or more populations when the populations are identified by only a subset of the parameters of the model. The generalized discriminant function is used to define a generalized discriminant statistic and an observation with an unknown treatment effect is classified according to the value of this statistic. Properties of this statistic are presented and these results are used to define classes of sample and asymptotic decision rules. Various criteria for selecting a decision rule from these classes are investigated. In particular, with respect to the probability of misclassification, the best asymptotic decision rule using the generalized discriminant statistic is identified and it is shown that if the populations are collinear then this decision rule is optimal. A numerical study provides an asymptotic evaluation of the proposed decision rule when the populations are not collinear.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1969
- Accession Number
- AD0690223
Entities
People
- Harry O. Posten
- Leigh Harrington
Organizations
- University of Connecticut