|Title||Hochberg Multiple Test Procedure Under Negative Dependence|
|Year of Publication||2014|
|Authors||Gou, J, and AC Tamhane|
The Hochberg (1988) procedure is commonly used in practice to test multiple hypotheses based on their p-values. It is a conservative step-up shortcut to the closed procedure (Marcus et al. 1976) based on the Simes (1986) test, which is exact when the p -values are independent. Sarkar and Chang (1997) and Sarkar (1998) have shown that the Simes test is conservative if the test statistics are positively dependent in a certain sense, so the Hochberg procedure is also conservative. On the other hand, Block et al. (2008) have shown that the Simes test is anti-conservative if the test statistics are negatively dependent. This had also been shown previously in the case of negatively correlated bivariate normal test statistics by Hochberg and Rom (1995) and Samuel-Cahn (1996). So practitioners are weary of using the Hochberg procedure in these latter cases. We show that the Hochberg procedure, being conservative by construction for independent p -values, remains conservative under many negative dependent distributions. Therefore its use can be advocated more widely.
Hochberg Multiple Test Procedure Under Negative Dependence