Contributions to Statistical Modeling for Complex Longitudinal and Multivariate Time Series Data

Abstract

Repeated measurements data are commonly encountered in numerous fields, including medical research, economics, material science, and engineering. While the statistical analysis of such datasets poses challenges due to their complex dependency structures, they also offer opportunities for more detailed understanding of relationships and temporal development both between and within observational units. There are well-founded statistical methods for the analysis of repeated measurements data in the statistical literature.However, real-world data often contain outlying or unusual observations that do not align with the imposed model structure. If not properly accounted for, such deviations can significantly impact the accuracy of statistical analyses, bias or invalidate the results. Identifying the outlying observations is important and can contribute to a deeper understanding of the data and underlying structures. Furthermore, particularly in long observation periods,changes in the environment or structural shocks can alter model parameters and relationships.Traditional models with fixed parameters may therefore no longer be suitable, and it becomes necessary to account for parameter variation within the model. Analyzing the resulting parameter dynamics can yield valuable insights into the structural changes that occur overtime.This thesis addresses the issues mentioned above by developing models tailored to different types of repeated measurements data: multivariate time series and longitudinal (functional)data. We propose a time-varying parameter reduced-rank regression model for multivariate time series regression, a robust estimation method for mixed effects models in the presence of outlying responses and predictors, and a robust estimation algorithm for marginal principal components analysis of longitudinally observed functional datasets. The effectiveness of the developed models and estimation methods is demonstrated through simulation studies. Furthermore, the three methods are illustrated in real-world data applications from various fields.