Statistical Inference on Sets, Nonparametric Financial Time Series and Extreme Value theory

该项目由两部分组成：对集合的统计推断和非参数金融时间序列。第一个主题是非参数集的置信区域。构造是基于非参数曲线估计。在数学上，这需要分析光滑估计量在流形上的上界分布。感兴趣的集合包括曲线、脊线、曲线的交点和交点边界的水平集。这样的集合产生于不同的应用领域。第二个主题是类似garch的金融时间序列的构造，其中动态运行在随机递归方程上，但不是条件方差，而是其他条件非参数函数进入模型。极值统计用于分析结果时间序列和其他已经研究过的garch过程的尾部行为。

The project consists in two parts: statistical inference on sets and nonparametric financial time series. The first topic is confidence regions for nonparametric sets. The construction is based on nonparametric curve estimators. Mathematically, this requires the analysis of the distribution of suprema of smoothing estimators over manifolds. Sets of interest are e.g. level sets of curves, ridges, intersections of curves, and intersection bounds. Such sets arise from different fields of applications. The second topic is the construction of GARCH-like financial time series where the dynamics runs over a stochastic recurrence equation but where instead of conditional variances also other conditional nonparametric functionals enter into the model. Extreme value statistics is used to analyse the tail behaviour of the resulting time series and of other already studied GARCH-processes.