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Multivariate Functional Halfspace Depth

Author

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  • Gerda Claeskens
  • Mia Hubert
  • Leen Slaets
  • Kaveh Vakili

Abstract

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.

Suggested Citation

  • Gerda Claeskens & Mia Hubert & Leen Slaets & Kaveh Vakili, 2014. "Multivariate Functional Halfspace Depth," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 411-423, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:411-423
    DOI: 10.1080/01621459.2013.856795
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