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Large‐scale multiple testing under dependence
Author(s) -
Sun Wenguang,
Tony Cai T.
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00694.x
Subject(s) - false discovery rate , multiple comparisons problem , oracle , computer science , null hypothesis , constraint (computer aided design) , statistical hypothesis testing , data mining , markov chain , algorithm , mathematical optimization , mathematics , econometrics , machine learning , statistics , biochemistry , chemistry , geometry , software engineering , gene
Summary. The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two‐state hidden Markov model. We propose oracle and asymptotically optimal data‐driven procedures that aim to minimize the false non‐discovery rate FNR subject to a constraint on the false discovery rate FDR. It is shown that the performance of a multiple‐testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses, and hence conventional FDR procedures that ignore this structural information are inefficient. Both theoretical properties and numerical performances of the procedures proposed are investigated. It is shown that the procedures proposed control FDR at the desired level, enjoy certain optimality properties and are especially powerful in identifying clustered non‐null cases. The new procedure is applied to an influenza‐like illness surveillance study for detecting the timing of epidemic periods.