  The statistical analysis of functional data is a growing need in many
research areas. In particular, a robust methodology is important to study
curves, which are the output of experiments in applied statistics. In this
paper we study some new definitions which reflect the "extremality" of a curve
with respect to a collection of functions, and provide natural orderings for
sample curves. Their finite dimensional versions are computationally feasible
and useful for studying high dimensional observations. Thus, these extreme
measures are suitable for complex observations such as microarray data and
images. We show the applicability of these measures designing a rank test for
functional data. This functional rank test shows different growth patterns for
boys and girls when it is applied to children growth data.
