  A functional data depth provides a center-outward ordering criterion which
allows the definition of measures such as median, trimmed means, central
regions or ranks in a functional framework. A functional data depth can be
global or local. With global depths, the degree of centrality of a curve $x$
depends equally on the rest of the sample observations, while with local
depths, the contribution of each observation in defining the degree of
centrality of $x$ decreases as the distance from $x$ increases. We empirically
compare the global and the local approaches to the functional depth problem
focusing on three global and two local functional depths. First, we consider
two real data sets and show that global and local depths may provide different
insights. Second, we use simulated data to show when we should expect
differences between a global and a local approach to the functional depth
problem.
