Longitudinal Functional Data Methods for Emerging Repeated Measurements

In recent years, longitudinal studies increasingly collect data where the primary measurements are functions or surfaces observed repeatedly over time. This talk introduces parsimonious modeling frameworks for such functional data, designed to extract meaningful low-dimensional features while respecting the longitudinal design. The methodology is computationally efficient and well-suited for characterizing the dynamic evolution of the underlying process. We then extend the framework to accommodate pointwise skewness in the data, broadening its applicability. Building on the key ideas, we discuss inference in the form of significance tests for hypotheses of scientific interest in this setting. We conclude by highlighting several open challenges and emerging directions in the analysis of longitudinal functional data.