Rejoinder: On Methods Controlling the False Discovery Rate

The false discovery rate of Benjamini and Hochberg has a great influence in shaping modern statistical theory. Besides its relevance and utility in contemporary statistical applications, there is mathematical elegance in its theory that is fascinating and has motivated me, just as it it did many others, I am sure, toward its further development and meaningful extension. I try to bring out this elegance in the paper by presenting some important results on FDR with different proofs and insights, in addition to offering a possible extension of the theory of FDR to correlated test statistics. I am delighted to see that the discussants, Professor P. K. Sen and Professors Romano, Shaikh and Wolf, reacted positively to my paper. I thank them for their complimentary and encouraging comments and making interesting observations on how the theory of FDR could potentially be enriched in light of the results presented in the paper. I must, however, mention that there are several other important results on the FDR that I have not been able to present in this paper. Moreover, as Gilles Blanchard has pointed out when I requested him to comment on the final draft of this paper that somewhat similar tools were used independently in other recent papers in proving some of the same results presented here; see Blanchard and Roquain (2008) which has been revised more recently after this paper is written and is avaialable at http://arxiv.org/abs/0707.0536.