The project focusses on modelling distributional properties with expectiles and investigates practical, theoretical and numerical properties.

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The project aims at the modelling of distributional properties using non-parametric estimates. Classical non-parametric (mean-) regression will be extended to expectile regression. This allows to model the entire conditional distribution of a response variable instead of the mean value only. Numerous results from penalized spline estimation will be adapted to expectile regression which allows to derive asymptotic properties for the estimates. A particular modelling exercise is laid upon expectile estimation for longitudinal, clustered data. The dependence structure in the data is captured by incorporating individual components in the model, extending (linear) mixed models to mixed expectile models. Expectiles will also be compared and contrasted to quantiles serving as established benchmark model.All results of the project will be made available numerically with R packages.