# Statistical discrimination analysis

Elbishti, Farouk (1968) Statistical discrimination analysis. MSc(R) thesis, University of Glasgow.

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## Abstract

In this thesis a critical survey of techniques of statistical discrimination is undertaken. The problem of statistical discrimination arises where previous work has separated a number of individuals into k distinct classes, there being available on each individual a vector of m-measurements. The problem is to assign a new unclassified individual for which the vector of m-measurements is available, to one of the k classes. Many different techniques for solving this problem have been suggested and these are considered in Chapters 2-5 of the thesis.The idea of classical techniques (Chapter 2) is to find a linear combination of the m-measurements and use its value for the allocation of the new individual. This idea is derived from the assumption of normality of the variability of the data for the different classes. The technique was introduced by Fisher (1936). Another technique, called Bayesia discrimination (Chapter 3) requires some prior information about the relative frequencies the different classes which, after the observation of the new individual, can be converted into a posterior information by the use of Bayes's theorem. The main developments of this theory to data require knowledge of the distributions of the different classes. Some techniques - order-statistic and convex-hull methods (Chapter 4) have recently been introduced by Kendall (1965). For the first method the discrimination procedure is built up in stages. A first step towards discrimination is taken by considering the measurements one at a time, and using that measurement which separates into classes the most individuals.At subsequent stages only previously unclassified individuals and unused measurements are considered in the search for the further refinement of the procedure. The second method consists of constructing the convex-hull of each class and allocating the new individual if aid only if it falls in one of the convex-hulls.Other recent techniques have been introduced by Sebestyen (1962) and are termed similarity index procedures (Chapter 5). The idea underlying this theory is to calculate the similarity of the irdividual to each dass and allocate it to the class which is most similar. The concept of measuring similarity which is suggested by Sebestyen is the calculation of the mean-square distance between a point and a class of points.The main conclusion (Chapter 6) is that there is no general procedure which can be followed in every situation. The application of any technique depends on the nature of the practical problem.The hope of obtaining improved procedures seems to lie in the use of large scale computers to provide in some convenient form a geometric picture of the high-dimensional data involved in most practical problems.

Item Type: Thesis (MSc(R)) Masters Adviser: J Aitchison Statistics 1968 Enlighten Team glathesis:1968-74157 Copyright of this thesis is held by the author. 23 Sep 2019 15:33 23 Sep 2019 15:33 http://theses.gla.ac.uk/id/eprint/74157