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Activity Number:
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380
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Type:
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Contributed
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Date/Time:
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Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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ENAR
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| Abstract - #309885 |
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Title:
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Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control
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Author(s):
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Wenguang Sun*+ and Tony Cai
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Companies:
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University of Pennsylvania and University of Pennsylvania
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Address:
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503 Blockley Hall 423 Guardian Drive, Philadelphia, PA, 19104,
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Keywords:
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Adaptive procedure ; compound decision rule ; false discovery rate
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Abstract:
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We develop a compound decision theory framework for multiple testing problems and derive an oracle rule based on the $z$-values that minimizes the false non-discovery rate (FNR) subject to a constraint on the false discovery rate (FDR). It is shown that many commonly used multiple testing procedures, which are $p$-value based, are inefficient. An adaptive procedure based on the $z$-values is proposed. It is shown that the $z$-value based adaptive procedure asymptotically attains the performance of the $z$-value oracle procedure and is more efficient than the conventional $p$-value based methods. Numerical performance of the adaptive procedure is investigated using both simulated and real data. In particular our method is demonstrated in an analysis of the microarray data from a HIV study that involves testing a large number of hypotheses simultaneously.
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