Resumen de Adaptive and depth buffer solutions with bundles of parallel rayls for global line Montecarlo radiosity

Elfego Martinez Ramirez Roel

• Survival analysis deals with the evaluation of variables which measure the elapsed time until an event of interest. One particularity survival analysis has to account for are censored data, which arise whenever the time of interest cannot be measured exactly, but partial information is available. Four types of censoring are distinguished: right-censoring occurs when the unobserved survival time is bigger, left-censoring when it is less than an observed time, and in case of interval-censoring, the survival time is observed within a time interval.

  We speak of doubly-censored data if also the time origin is censored.

  Methods for interval-censored data have received much attention during the last decades, however a topic, which has hardly been addressed in scientic literature, is the case of interval-censored covariates in regression models.

  An exception is the work of Gomez, Espinal and Lagakos (2003) who present a linear regression model with such a covariate.

  Therefore, an important part of this PhD thesis will be dedicated to estimation procedures for parametric survival models with an interval-censored covariate.

  In Chapter 1 of the thesis, we rst give a survey on statistical methods for intervalcensored data, including both parametric and nonparametric approaches. Most of these procedures are based on the assumption that the censored data generating process is noninformative.

  That means that the observed intervals do not carry any further information on the unobserved survival time. Without this assumption, the construction of the likelihood function would have to account for the censoring process, and the distribution function of the survival time could not be identied.

  In the second part of Chapter 1, we address this important issue with more detail. Given the importance of optimization procedures in the further chapters of the thesis, the nal section of Chapter 1 is about optimization theory.

  This includes some optimiz