Flexible hazard-based models and quantile regression for right-censored data using two-piece asymmetric distributions

This project aims at developing new methodologies for statistical inference for flexible mean and quantile regression models based on complex data, in particular censored data. The emphasis in this research will be on inference for quantiles, including quantile regression. In recent years, a few large asymmetric families of distributions have been studied. The interesting feature of these families is that the location parameter coincides with a specific quantile of the distribution. In the special case of a symmetric distribution, the location parameter coincides with the mean. One of the considered families parallels the framework of generalized linear models, but from a quantile perspective. Extensions to a regression setting have been and are part of recent and ongoing research. In many applications an important complexity is that only partial information on the variables of interest is observed. Among such complex data settings are censored data, occurring in particular in survival analysis where, in a right random censorship context, it is only known -- for some of the studied objects -- that the survival time of interest exceeds the observed time. The focus in this project will be on statistical inference for quantiles based on partial observations, and allowing for flexible modelling.