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Fenske, Nora (2012): Structured additive quantile regression with applications to modelling undernutrition and obesity of children. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics



Quantile regression allows to model the complete conditional distribution of a response variable - expressed by its quantiles - depending on covariates, and thereby extends classical regression models which mainly address the conditional mean of a response variable. The present thesis introduces the generic model class of structured additive quantile regression. This model class combines quantile regression with a structured additive predictor and thereby enables a variety of covariate effects to be flexibly modelled. Among other components, the structured additive predictor comprises smooth non-linear effects of continuous covariates and individual-specific effects which are particularly important in longitudinal data settings. Furthermore, this thesis gives an extensive overview of existing approaches for parameter estimation in structured additive quantile regression models. These approaches are structured into distribution-free and distribution-based approaches as well as related model classes. Each approach is systematically discussed with regard to the four previously defined criteria, (i) which different components of the generic predictor can be estimated, (ii) which properties can be attributed to the estimators, (iii) if variable selection is possible, and, finally, (iv) if software is available for practical applications. The main methodological development of this thesis is a boosting algorithm which is presented as an alternative estimation approach for structured additive quantile regression. The discussion of this innovative approach with respect to the four criteria points out that quantile boosting involves great advantages regarding almost all criteria - in particular regarding variable selection. In addition, the results of several simulation studies provide a practical comparison of boosting with alternative estimation approaches. From the beginning of this thesis, the development of structured additive quantile regression is motivated by two relevant applications from the field of epidemiology: the investigation of risk factors for child undernutrition in India (by a cross-sectional study) and for child overweight and obesity in Germany (by a birth cohort study). In both applications, extreme quantiles of the response variables are modelled by structured additive quantile regression and estimated by quantile boosting. The results are described and discussed in detail.