G-2002-57
An Affine-Invariant Multivariate Sign Test for Cluster Correlated Data
référence BibTeX
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.
Paru en octobre 2002 , 26 pages