A weighted spatial median for clustered data

Jaakko Nevalainen (), Denis Larocque () and Hannu Oja ()
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Jaakko Nevalainen: University of Tampere
Denis Larocque: HEC Montréal 3000 chemin de la Côte-Sainte-Catherine, Montréal (Québec)
Hannu Oja: University of Tampere

Statistical Methods & Applications, 2007, vol. 15, issue 3, No 6, 355-379

Abstract: Abstract A weighted spatial median is proposed for the multivariate one-sample location problem with clustered data. Its limiting distribution is derived under mild conditions (no moment assumptions) and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and the theoretical results are supplied with illustrative examples. It turns out that there is a potential for meaningful gains in estimation efficiency: the weighted spatial median has superior efficiency to the unweighted spatial median particularly when the cluster sizes are widely disparate and in the presence of strong intracluster correlation. The unweighted spatial median for clustered data was considered earlier by Nevalainen et al. (Can J Statist, in press, 2007). The proposed weighted estimators provide companion estimates to the weighted affine invariant sign test proposed recently by Larocque et al. (Biometrika, in press, 2007). An affine equivariant weighted spatial median is discussed in parallel.

Keywords: Multivariate one-sample location problem; Spatial median; Clustered data; Intracluster correlation; Sign correlation; Breakdown point (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10260-006-0031-7

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