Stochastic Approximation for Multivariate and Functional Median

Hervé Cardot (), Peggy Cénac () and Mohamed Chaouch ()
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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

A chapter in Proceedings of COMPSTAT'2010, 2010, pp 421-428 from Springer

Abstract: 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.

Keywords: geometric quantiles; high dimension data; online estimation algorithm; robustness; Robbins-Monro; spatial median; stochastic gradient averaging (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2604-3_40

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DOI: 10.1007/978-3-7908-2604-3_40

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