title: A test of location for exchangeable multivariate normal data with unknown correlation.
abstract: We consider the problem of testing whether the common mean of a single n-vector of multivariate normal random variables with known variance and unknown common correlation ρ is zero. We derive the standardized likelihood ratio test for known ρ and explore different ways of proceeding with ρ unknown. We evaluate the performance of the standardized statistic where ρ is replaced with an estimate of ρ and determine the critical value c(n) that controls the type I error rate for the least favorable ρ in [0,1]. The constant c(n) increases with n and this procedure has pathological behavior if ρ depends on n and ρ(n) converges to zero at a certain rate. As an alternate approach, we replace ρ with the upper limit of a (1 - β(n)) confidence interval chosen so that c(n) = c for all n. We determine β(n) so that the type I error rate is exactly controlled for some ρ in [0,1]. We also investigate a simpler approach where we bound the type I error rate. The former method performs well for all n while the less powerful bound method may be a useful in some settings as a simple approach. The proposed tests can be used in different applications, including within-cluster resampling and combining exchangeable p-values.
authors: Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 6700B Rockledge Drive MSC 7609, Bethesda, MD 20892.
authors: Dean
authors: D
authors: Follmann
authors: Michael
authors: M
authors: Proschan