Mathematics

Functional Data Analysis is a powerful framework for analyzing high-dimensional data that represent phenomena evolving over continuous domains. This field has seen significant advancements in recent years, spurring the development of novel statistical methodologies and the adaptation of classical multivariate techniques to the functional setting. However, a critical challenge arises when functional data are only partially observed over their domain of definition, as many established techniques cannot be directly applied in such scenarios. We focus on extending the functional linear regression model to accommodate partially observed functional data. The proposed approach involves reconstructing the incomplete data and performing a weighted functional data analysis, where observation-specific weights are used to reflect the uncertainty associated with the reconstructed portions of the functional data. The methodology proves useful in the field of seismic hazard assessment, where it is employed to develop a new functional Ground Motion Model for Italy.