Abstract
Ph.D. (Mathematical Statistics)
Diagnostic tests are often used to classify a population into distinct groups. The ability of
a diagnostic test to perform this classi…cation with a high degree of accuracy is of immense
practical bene…t. The Ordinal Dominance Curve (ODC) is a standard tool used to evaluate the
performance of a diagnostic test with regards to its ability to distinguish between dichotomous
outcome categories. In this thesis, we explore various aspects of the ODC and develop extensions
and improvements of the existing methodology.
Non-parametric and semi-parametric approaches to estimating the ODC are discussed. We
simplify some of the existing semi-parametric estimation methods and establish a method that
leads to easily computable estimators and associated standard errors.
In the literature the binormal model is the most common semi-parametric representation of the
ODC. We establish a procedure, along the lines of the well known quantile-quantile (Q-Q) plots,
for assessing the validity of the binormal assumption. The literature is relatively sparse regarding
this aspect of the binormal model. We therefore delve deeper into assessing the appropriateness
of this assumption with a particular focus on understanding its underlying properties.
To express the precision and describe the level of uncertainty of the ODC estimate, con…dence
band approaches are adopted. We contribute to the literature by presenting new semi-parametric
and non-parametric con…dence bands for the ODC.
Methods used to compare two ODCs are discussed. We propose a permutation approach using
two alternate test statistics that aims to address some of the weaknesses of the currently adopted
methods.
Simulation studies are conducted to assess the performance of the proposed and existing methods
discussed in the thesis. We apply our procedures to actual credit risk data to demonstrate the
practical relevance of the proposed methods.