Abstract |
: |
In many studies in medicine, economics, demography, sociology, education, among others, one is often interested in the time until a certain event happens. This time can be the time until a patient dies or recovers from a disease (in a medical study), the time until an unemployed person finds a new job (in economics), the age at which a person marries (in demography), the time until a released prisoner gets re-arrested (in sociology), or the time taken to solve a problem (in education). The analysis of data of this kind is commonly called ‘survival analysis’ (or ‘duration analysis’ depending on the area of application). For this type of data it is common to be right censored. A typical assumption when working with randomly right censored data, is the independence between the variable of interest Y (the survival time) and the censoring variable C. This assumption, which is not testable, is however unrealistic in certain situations. In this thesis we assume that for a given covariate X, the dependence between the variables Y and C is described via a known copula. Additionally we assume that Y is the response variable of a heteroscedastic regression model Y = m(X) + σ(X)ε, where the error term ε is independent of the explanatory variable X, and the functions m and σ are ‘smooth’. Under this model we propose estimators of the functionals m(•) and σ(•), and of the conditional distribution of Y given X. We focus on studying asymptotic properties and small sample performance of these estimators. |