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建立分布特性模型。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建模，而不是仅对平均值建模。惩罚样条估计的许多结果将适应于期望回归，从而可以获得估计的渐近性质。一个特定的建模练习奠定了预期的估计纵向，聚类数据。数据中的依赖结构是通过在模型中加入单个组件来捕获的，将（线性）混合模型扩展到混合预期模型。期望值也将与作为既定基准模型的分位数进行比较和对比。项目的所有结果将通过R软件包以数字形式提供。

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.