Asymptotic Optimality of Multiple Hypothesis Testing Procedure in Equi-correlated Set-up

In this paper, we have used subset selection approach to select the significant hypotheses in the context of multiple hypothesis testing problem, stated in [1]Bogdan, Chakrabarty, Frommlet and Ghosh(2011). The above paper considers the problem of identifying the hypotheses which correspond to greater variance of normal variate in an independent set up, and they have considered the problem for dependent normal variables (in particular for equi-correlated set up) to be an open problem. We have explored the problem both theoretically and through extensive simulations. We have found asymptotically optimal procedure for the equi-correlated case. Though in the above mentioned paper the results were done in the context of sparsity, our results are considered under sparsity and also for the general case.