On the multivariate spatial median for clustered data

The authors consider the multivariate one‐sample location problem with clustered data from a nonparametric viewpoint. They propose the spatial median and its affine equivariant version as companion estimators to the affine invariant sign test of Larocque (2003). They extend the asymptotics of the proposed estimators to cluster dependent data and explore the limiting as well as finite‐sample efficiencies for multivariate Student distributions. They demonstrate that the efficiency of the spatial median suffers less from intracluster correlation than the mean vector. They use data on the well‐being of pupils in Finnish schools to illustrate their work.