Quantile regression for twice and doubly censored data

• Applicant: Dr. Stanislav Volgushev
• Subject Area: Mathematics
• Term: from 2011 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 206326820

A central aim of mathematical statistics consists in describing how certain covariates (for example the dose of a drug) influence a dependent variable T (for example the time of recovery from a disease). A complete characterization of such dependencies can be obtained from the distribution of T for fixed covariate values. Mathematically it is described by the conditional distribution function. Often only certain aspects of such distributions, as for example the influence of covariates on atypically high response values, are of interest. An elegant way to describe this kind of dependencies is provided by the method of quantile regression. In many situations, as for example medical studies, some of the response values are not fully observed. For example, it might happen that the time from outbreak to recovery from a disease T is only known to be larger or smaller than a given time R (duration of study) or L (time from first diagnosis to recovery), respectively. Such data are commonly called doubly censored.Only few methods for quantile regression that are applicable to doubly censored data are available to date, and all the existing estimators require restrictive assumptions on the underlying data structure. The main goal of the proposed research project is the development of statistical procedures for the analysis of doubly censored data that do not need such assumptions. The first aim is to obtain estimators for the conditional distribution function. The second aim is the development of methods for quantile regression. Here, two different classes of assumptions need to be considered. First, conditional quantile estimation under general smoothness conditions needs to be treated. The advantage of this approach lies in its broad applicability. Second, parametric regression quantile estimators need to be constructed. The advantage of parametric estimation procedures lies in their greater precision, at least as long as the underlying model is specified correctly.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Roger Koenker