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Multivariate functional halfspace depth. (English) Zbl 1367.62162

Summary: This article defines and studies a depth for multivariate functional data. 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. We study both population and finite sample versions. 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. We present a simulation study and data examples that confirm the good performance of this depth function.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62G05 Nonparametric estimation
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