Integrated Depths for Partially Observed Functional Data

Partially observed functional data are frequently encountered in applications and the object of an increasing interest by literature. We here address problem measuring centrality a datum partially sample. propose integrated depth for data, dealing with very challenging case where partial observability can occur systematically on any observation dataset. In particular, differently from many techniques we do not request that some is fully observed, nor require common domain exist, all recorded. Because this, our proposal also be used those frequent situations reconstructions methods other inapplicable. By means simulation studies, demonstrate good performances proposed finite samples. Our enables use benchmark based depths, originally introduced data. This includes boxplot, outliergram versus classifiers. illustrate two first concerning outlier detection German electricity supply functions, second regarding classification obtained medical imaging. Supplementary materials this article available online.