Statistische Methoden für Longitudinale Funktionale Daten

点击翻译按钮获取中文摘要

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.