Groupe d’études et de recherche en analyse des décisions

G-2007-108

A Weighted Multivariate Signed-Rank Test for Cluster-Correlated Data

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A weighted multivariate signed-rank test is introduced for an analysis of multivariate clustered data. Observations in different clusters may then get different weights. The test provides a robust and efficient alternative to normal theory based methods. Asymptotic theory is developed to find the approximate p-value as well as to calculate the limiting Pitman efficiency of the test. A conditionally distribution-free version of the test is also discussed. The finite-sample behavior of different versions of the test statistic is explored by simulations and the new test is compared to the weighted versions of Hotelling’s T2 test and the multivariate spatial sign test introduced in Larocque et al. (2007). Finally, a real data example is used to illustrate the theory.

, 26 pages