Archive
Special Issues Volume 9, Issue 6, December 2020, Page: 124-128
Annotations on the Relationship Among Discriminant Functions
Awogbemi Clement Adeyeye, Department of Statistics, National Mathematical Centre, Abuja, Nigeria
Received: Jun. 19, 2020;       Accepted: Jul. 20, 2020;       Published: Dec. 16, 2020
Abstract
Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Ever since the emergence of the Linear Discriminant Function (LDF) by Fisher, several other classification statistics have emerged and violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). While the Best Linear Discriminant Function (BLDF) is referred to Best Sample Discriminant Function (BSDF) when the parameters are estimated from a sample and also optimal in the same sense as Quadratic Discriminant Function (QDF), Rao statistic is best for discriminating between options that are close each other. The relationships among the classification statistics examined were established: Among the methods of classification statistics considered, Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes n1 and n2 are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification.
Keywords
Discriminant Functions, Classification Statistics, Classification Problems, Covariance Matrix, Probability of Misclassification
Awogbemi Clement Adeyeye, Annotations on the Relationship Among Discriminant Functions, Pure and Applied Mathematics Journal. Vol. 9, No. 6, 2020, pp. 124-128. doi: 10.11648/j.pamj.20200906.14
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