| The false discovery rate (FDR) introduced by Benjamini and Hochberg (1995) is perhaps the most standard error controlling measure being used in a wide variety of applications involving multiple hypothesis testing. There are two approaches to control the FDR - the fixed error rate approach of Benjamini and Hochberg (1995) where a rejection region is determined with the FDR below a fixed level and the estimation based approach of Storey (2002) where the FDR is estimated for a fixed rejection region before it is controlled. In this dissertation, we concentrate on both these approaches and propose new, improved versions of some FDR controlling methods available in the literature.;A number of adaptive methods have been put forward in the literature, each attempting to improve the method of Benjamini and Hochberg (1995), the BH method, by incorporating into this method an estimate of n 0, the unknown number true null hypotheses. Among these, the method of Benjamini, Krieger and Yekutieli (2006), the BKY method, has been receiving a lot of attention recently. In this dissertation, a variant of the BKY method is proposed by considering a different estimate of n 0, which often outperforms the BKY method in terms of the FDR control and power.;Storey's (2002) estimation based approach to controlling the FDR has been developed using a class of conservatively biased point estimates of the FDR under a mixture model for the underlying p-values and a fixed rejection threshold for each null hypothesis. An alternative class of point estimates of the FDR with uniformly smaller conservative bias is proposed under the same setup. Numerical evidence is provided to show that the mean squared error (MSE) is also often smaller for this new class of estimates. Storey's (2002) q-value method has been modified based on this new class of point estimates of the FDR, which appears to be more powerful than Storey's original q-value method. |
