Functional data analysis (FDA) has become a vital tool in statistics, particularly effective when data points are densely sampled. Here, it offers a significant advantage over traditional Repeated Measures and MAN(C)OVA techniques by not assuming specific correlation structures or requiring evenly spaced data points. This flexibility can lead to more robust inference and enables the extraction of additional information from the data. Despite methodological advancements, there is still a need for robust FDA methods to handle challenges such as missing data, non-Gaussianity, and covariance function heteroscedasticity.

This project aims to develop new methods for both univariate and multivariate functional repeated measures ANOVA and ANCOVA that are not constrained by traditional model assumptions. These methods will be designed to provide reliable results even in challenging settings characterized by small sample sizes and partially or completely missing observations. They will also support the inclusion of covariate adjustments within various factorial designs and will be capable of addressing complex hypotheses involving main and interaction effects in both crossed and hierarchical models without relying on a specific distribution.

To this end, the project will utilize both traditional and novel estimators, such as functional sample or wavelet estimators for mean and covariance functions. These will be combined with a range of inference approaches, including projection-based and multiple contrast type statistics, to create a flexible and robust statistical framework. These methods will undergo rigorous evaluation through simulations, mathematical analyses, and practical applications to ensure their theoretical soundness and practical viability.

The collaborative effort involves the two principal investigators, their teams, and two renowned Mercator Fellows. This cooperation will not only advance the development of FDA methods, focusing on testing and confidence regions, but also enhance FDA application guidelines specifically tailored to meet biostatistical needs. This comprehensive approach aims to bridge the gap between advanced statistical theory and real-world applications, making it a significant step forward in the field of functional data analysis.