Mathematics – Statistics Theory
Scientific paper
2009-06-17
Annals of Statistics 2009, Vol. 37, No. 3, 1518-1544
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/08-AOS616 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/08-AOS616
The most popular multiple testing procedures are stepwise procedures based on $P$-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini--Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300] and their offsprings. Even for models that entail dependent data, $P$-values based on marginal distributions are used. Unlike such methods, the new method takes dependency into account at all stages. Furthermore, the $P$-value procedures often lack an intuitive convexity property, which is needed for admissibility. Still further, the new methodology is computationally feasible. If the number of tests is large and the proportion of true alternatives is less than say 25 percent, simulations demonstrate a clear preference for the new methodology. Applications are detailed for models such as testing treatments against control (or any intraclass correlation model), testing for change points and testing means when correlation is successive.
Cohen Arthur
Sackrowitz Harold B.
Xu Minya
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