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Stochastic Approximation for Multivariate and Functional Median

In: Proceedings of COMPSTAT'2010

Author

Listed:
  • Hervé Cardot

    (Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 CNRS)

  • Peggy Cénac

    (Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 CNRS)

  • Mohamed Chaouch

    (EDF - Recherche et Développement, ICAME-SOAD)

Abstract

We propose a very simple algorithm in order to estimate the geometric median, also called spatial median, of multivariate (Small (1990)) or functional data (Gervini (2008)) when the sample size is large. A simple and fast iterative approach based on the Robbins-Monro algorithm (Duflo (1997)) as well as its averaged version (Polyak and Juditsky (1992)) are shown to be effective for large samples of high dimension data. They are very fast and only require O(Nd) elementary operations, where N is the sample size and d is the dimension of data. The averaged approach is shown to be more effective and less sensitive to the tuning parameter. The ability of this new estimator to estimate accurately and rapidly (about thirty times faster than the classical estimator) the geometric median is illustrated on a large sample of 18902 electricity consumption curves measured every half an hour during one week.

Suggested Citation

  • Hervé Cardot & Peggy Cénac & Mohamed Chaouch, 2010. "Stochastic Approximation for Multivariate and Functional Median," Springer Books, in: Yves Lechevallier & Gilbert Saporta (ed.), Proceedings of COMPSTAT'2010, pages 421-428, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2604-3_40
    DOI: 10.1007/978-3-7908-2604-3_40
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