Statistische Methoden für Longitudinale Funktionale Daten

科学研究越来越多地收集数据，其中每次观察都由曲线或图像组成。从脑电图、成像技术、电子商务等方面的常规数据收集，产生的功能数据越来越大，越来越复杂。这个项目的目标是建立在功能和纵向数据分析的基础上，为随时间重复观察的功能数据开发统计方法。为了对函数的静态和动态行为进行建模和信息提取，我们将基于功能主成分分析方法建立一类新的模型。这将允许我们将参数线性混合模型以及使用稀疏功能数据分析的纵向轮廓的非参数分析扩展到纵向功能数据的设置。我们将处理密集采样和稀疏采样的函数和图像。基于这种方法，我们可以扩展功能回归模型来模拟时不变或纵向结果对纵向功能预测因子的依赖性。将开发统计方法，重点是计算可行性和开源实现，用于现在常规收集的非常大的数据集。

Scientific studies increasingly collect data where each observation consists of a curve or image. Routine collection of data from EEG, imaging techniques, electronic commerce, to name just a few, yields functional data of increasing size and complexity. The goal of this project is to develop statistical methodology for functional data that is observed repeatedly over time, building on work in both functional as well as longitudinal data analysis. To model and extract information on the static and the dynamic behavior of functions, we will build a new class of models based on functional principal components analysis methodology. This will allow us to extend both the parametric linear mixed model, as well as the nonparametric analysis of longitudinal profiles using sparse functional data analysis, to the setting of longitudinal functional data. We will address densely as well as sparsely sampled functions and images. Based on this approach, we can then extend functional regression models to model the dependency of time-invariant or longitudinal outcomes on longitudinal functional predictors. Statistical methods will be developed with a focus on computational feasibility and open source implementation for the very large data sets now routinely collected.