  John W. Tukey (1975) defined statistical data depth as a function that
determines centrality of an arbitrary point with respect to a data cloud or to
a probability measure. During the last decades, this seminal idea of data depth
evolved into a powerful tool proving to be useful in various fields of science.
Recently, extending the notion of data depth to the functional setting
attracted a lot of attention among theoretical and applied statisticians. We go
further and suggest a notion of data depth suitable for data represented as
curves, or trajectories, which is independent of the parametrization. We show
that our curve depth satisfies theoretical requirements of general depth
functions that are meaningful for trajectories. We apply our methodology to
diffusion tensor brain images and also to pattern recognition of hand written
digits and letters. Supplementary Materials are available online.
