Groupe d’études et de recherche en analyse des décisions


An Affine-Invariant Multivariate Sign Test for Cluster Correlated Data

A multivariate location model for cluster correlated observations is presented. An affine-invariant multivariate sign test for testing location is proposed. The test statistic is an adaptation of the one proposed by Randles (2000) and is asymptotically distributed as a 2 random variable under the null hypothesis under very mild conditions. In particular, the test can be used for skewed populations. The values of its Pitman asymptotic efficiency relative to a test based on the overall average are obtained for a general multivariate normal model. These results show that there is an improvement in the relative performance of the new test as soon as intra-cluster correlation is present. Even for one-dimensional data, the new test (based on signs in that case) can be very competitive at the normal model. Furthermore, the statistic is easy to compute even for large dimensional data. A simulation study shows that the test performs well in comparison to the average based test. An example with a real data set is also given.

, 26 pages