  Statistical depth is the act of gauging how representative a point is
compared to a reference probability measure. The depth allows introducing
rankings and orderings to data living in multivariate, or function spaces.
Though widely applied and with much experimental success, little theoretical
progress has been made in analysing functional depths. This article highlights
how the common $h$-depth and related statistical depths for functional data can
be viewed as a kernel mean embedding, a technique used widely in statistical
machine learning. This connection facilitates answers to open questions
regarding statistical properties of functional depths, as well as it provides a
link between the depth and empirical characteristic function based procedures
for functional data.
