The celebrated Storey adaptive multiple test of Storey, Taylor and Siegmund (2004) is frequently used to control the false discovery rate (FDR) beyond the classical Benjamini Hochberg test. However, Storey's rejection procedure relies on a prechosen value λ where an adequate estimator for the proportion of true p-values is evaluated at a single position λ.
The present talk establishes a device for a dynamic selection of λ's which yield more robust multiple tests. In particular these tests are controlling the FDR at each finite sample size. Also some extentions are discussed.
The second part presents a converse of the Benjamini Hochberg Theorem. Whenever the FDR is distribution free then the multiple test is already a Benjamini Hochberg test. This result works under mild regularity assumptions. The results are joint work with Philipp Heesen (Duesseldorf).
References:
1. Benjamini, Y. and Hochberg, Y. (1995). Controlling the False DiscoveryRate: A Practical and Powerful Approach to Multiple Testing. J. R. Stat.Soc. Ser. B Stat. Methodol. 57, no. 1, 289-300.
2. Sarkar S. K. (2008). On methods controlling the false discovery rate.Sankhya 70, no. 2, Ser. A, 135-168.
3. Storey J. D., Taylor J. and Siegmund D.(2004). Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unifi ed approach. J. R. Stat. Soc. Ser. B Stat.Methodol. 66, no. 1, 187-205.
4. Storey J. D. (2002). A direct approach to false discovery rates. J. R. Stat. Soc. Ser. B Stat. Methodol. 64, no. 3, 479-498.