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

该项目旨在利用非参数估计对分布特性进行建模。经典的非参数（均值）回归将扩展到期望回归。这允许对响应变量的整个条件分布进行建模，而不仅仅是平均值。惩罚样条估计的许多结果将适用于期望回归，从而可以导出估计的渐近性质。一个特殊的建模练习是建立在纵向的期望估计上的，聚类数据。通过合并模型中的单个组件，将（线性）混合模型扩展到混合预期模型，可以捕获数据中的依赖性结构。期望也将比较和对比作为建立基准模型的分位数。项目的所有结果都将在R包中以数字形式提供。

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.