Uncertainty in Discriminant Analysis

Hirst, David (1988) Uncertainty in Discriminant Analysis. PhD thesis, University of Glasgow.

Abstract

The aim of this thesis is to review and develop theory in discriminant analysis. In chapter one an example of medical diagnosis is considered, and two types of uncertainty are illustrated. Firstly, the log odds ratio can be close to zero, and secondly there can be considerable uncertainty about its true value. In chapter two we review existing methodology for constructing Interval estimates for the log odds when the two populations are normal. Five different methods are considered for distributions with equal covariances, and three are generalised to the unequal covariance situation. In chapter three these methods are Investigated by simulation. It is seen that only two methods in the equal covariance case give intervals of reliable empirical confidence, and only one generalises successfully to the unequal covariance case. In chapter four we go on to use the interval estimation methodology to assess a discriminant rule, suggesting some new ways of displaying the information available. In chapter five we develop the methods of chapter four to construct an accurate error rate estimator, which is compared with standard techniques by simulation. In chapter six the error rate estimator developed in chapter five is extended to the situation where there are more than two groups, and it is compared by simulation with generalisations of other standard techniques. The different methods are applied to a data set. In chapter seven the limitations of the work are discussed, and possible developments suggested.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Ian Ford
• Keywords: Statistics
• Date of Award: 1988
• Depositing User: Enlighten Team
• Unique ID: glathesis:1988-76493
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Nov 2019 14:16
• Last Modified: 19 Nov 2019 14:16
• URI: https://theses.gla.ac.uk/id/eprint/76493