Multivariate Functional Halfspace Depth

Gerda Claeskens

doi:10.1080/01621459.2013.856795

Multivariate Functional Halfspace Depth

2014-03-19

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DOI：10.1080/01621459.2013.856795

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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. Supplementary materials for this article are available online.

Keyword:

Functional data

Multivariate data

Statistical depth

Time warping

Multivariate Functional Halfspace Depth

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