  There has been a wide interest to extend univariate and multivariate
nonparametric procedures to clustered and hierarchical data. Traditionally,
parametric mixed models have been used to account for the correlation
structures among the dependent observational units. In this work we extend
multivariate nonparametric procedures for one-sample and several samples
location problems to clustered data settings. The results are given for a
general score function, but with an emphasis on spatial sign and rank methods.
Mixed models notation involving design matrices for fixed and random effects is
used throughout. The asymptotic variance formulas and limiting distributions of
the test statistics under the null hypothesis and under a sequence of
alternatives are derived, as well as the limiting distributions for the
corresponding estimates. The approach based on a general score function also
shows, for example, how $M$-estimates behave with clustered data. Efficiency
studies demonstrate practical advantages and disadvantages of the use of
spatial sign and rank scores, and their weighted versions. Small sample
procedures based on sign change and permutation principles are discussed.
Further development of nonparametric methods for cluster correlated data would
benefit from the notation already familiar to statisticians working under
normality assumptions.
