Flexible integrated functional depths

This paper develops a new class of functional depths. A generic member this is coined $J$th order $k$th moment integrated depth. It based on the distribution cross-sectional halfspace depth function in marginal evaluations (in time) random process. Asymptotic properties proposed depths are provided: we show that they uniformly consistent and satisfy an inequality related to law iterated logarithm. Moreover, limiting distributions derived under mild regularity assumptions. The versatility displayed by makes them particularly amenable for capturing important features distributions. illustrated supervised learning, where corresponding maximum classifiers outperform classical competitors.