Functional Depth for Partially Observable data on Multidimensional Domains

Michele Cavazzutti, Politecnico di Milano

Co-authors: Elenora Arnone, Dipartimento di Management, Università di Torino; Laura M. Sangalli, MOX Laboratory, Dipartimento di Matematica, Politecnico di Milano

Abstract: We introduce a depth measure for functional data defined over multidimensional domains, characterized by complex missing data patterns. Our approach utilizes a suitable geometrically-informed domain discretization method to estimate the integral in the functional depth definition. This choice effectively manages partial observability, even when the functional datum is missing over large portions of the domain. The proposed depth does not require prior reconstruction of the data. It also achieves desirable asymptotic statistical properties while exhibiting high computational efficiency. We illustrate our method with the study of Lake Victoria’s temperatures from the ARC-Lake database.