A weighted spatial median for clustered data

被引：3

作者：

Nevalainen J. ^{[1
]}

Larocque D. ^{[2
]}

Oja H. ^{[3
]}

机构：

[1] Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere

[2] Department of Quantitative Methods, HEC Montréal, Montréal, Que. H3T 2A7

[3] Tampere School of Public Health, University of Tampere, Tampere

来源：

Statistical Methods and Applications | 2007年 / 15卷 / 3期

基金：

加拿大自然科学与工程研究理事会; 芬兰科学院;

关键词：

Breakdown point; Clustered data; Intracluster correlation; Multivariate one-sample location problem; Sign correlation; Spatial median;

D O I：

10.1007/s10260-006-0031-7

中图分类号：

学科分类号：

摘要：

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. © 2006 Springer-Verlag.

引用

页码：355 / 379

页数：24

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