Some permutation symmetric multiple hypotheses testing rules under dependent setup

The problem of multiple hypothesis testing with correlated test statistics is a very important problem in statistical literature. Specifically, we consider the case when the joint distribution of the test statistics is a multivariate normal distribution with an unknown mean vector and compound symmetric correlation structure. Our goal is to identify nonzero entries of the mean vector. Bogdan et al. (2011) solved this problem when test statistics are independent normals along with the study of asymptotic optimality in a Bayesian decision theoretic sense. The case under dependence was left as a challenging open problem. The solution is intuitive and permutation invariant, does not assume sparsity unlike Bogdan et al. (2011) and is validated through simulation studies.