Multivariate Functional Halfspace Depth

A multivariate depth for functional data is defined and studied. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape and phase variation. Both population and finite sample versions are studied. The multivariate sample of curves may include warping functions, derivatives and integrals of the original curves for a better overall representation of the functional data via the depth. A simulation study and data example confirm the good performance of this depth function