Abstract
M.Sc. (Mathematical Statistics)
While a typical regression model describes how the mean value of a response variable varies with a set of explanatory variables, quantile regression describes the variation in the quantiles of the response. When the response distribution di ers substantially from normality the quantiles provide a substantially richer description of the distribution than can be obtained by standard regression, and is obtainable without making any assumptions on the form of the underlying distribution. In this dissertation we study the theory of quantile regression models, with particular focus on the application of quantile regression methods to censored survival data. While the statistical literature on censored quantile regression methods is extensive, the computational di culties and complicated inferential and asymptotic arguments associated with many of these approaches present a considerable stumbling block in the routine application of the methodology.
We discuss in detail a more recent approach which is based on counting processes and
martingale properties associated with counting processes. The inferential and asymptotic
properties of this method provides some notable advantages over comparable methods.
The performance of the method is examined using Monte Carlo Simulation, as well as an
application to a large loan portfolio of a nancial institution.