- Thesis:
- Master in Mathematics
- Author:
- Agnes Gambietz
- Title:
- Regression models for bounded responses with application to DNA methylation
- Supervisors:
- Jan JOHANNES and Dominic Edelmann (DKFZ)
- Abstract:
- The aim of this thesis is to provide an overview of regression models with focus on situations where the response variables are bounded. At this point, some important properties and solution strategies to problems that might thereby occur, such as heteroscedasticity and prediction of unreasonable values, are given. The parametric models that are being introduced are the classical linear regression model, the rank based regression model, the quantile regression model and the beta regression model. For the matter of boundedness, logit transformations of the response variables to (−∞,∞) are being discussed. Furthermore, a nonparametric regression approach with a transformation on the outcome variable involving an unknown parameter which provides more flexibility in formulating data relations, are examined and their asymptotic properties are proven under certain assumptions. Finally, as an application, the above-mentioned regression models are compared in a medical data study in terms of detecting significant associations between clinical covariates and methylation data bounded below by 0 and above by 1.
- Reference:
- O. Linton, S. Sperlich, and I. Van Keilegom. Estimation of a semiparametric transformation model. The Annals of Statistics, 36(2):686-718, 2008.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |