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Asymptotic theory of the spatial median

Jyrki Möttönen, Klaus Nordhausen, and Hannu Oja

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In this paper we review, prove and collect the results on the limiting behavior of the regular spatial median and its affine equivariant modification, the transformation retransformation spatial median. Estimation of the limiting covariance matrix of the spatial median is discussed as well. Some algorithms for the computation of the regular spatial median and its different modifications are described. The theory is illustrated with two examples.

Chapter information

J. Antoch, M. Hušková and P.K. Sen, eds., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 182-193

First available in Project Euclid: 29 November 2010

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Digital Object Identifier

Primary: 62H12: Estimation
Secondary: 62G05: Estimation 62G20: Asymptotic properties

asymptotic normality Hettmansperger–Randles estimate multivariate location spatial sign spatial sign test transformation retransformation

Copyright © 2010, Institute of Mathematical Statistics


Möttönen, Jyrki; Nordhausen, Klaus; Oja, Hannu. Asymptotic theory of the spatial median. Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, 182--193, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL718.

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