Institute of Mathematical Statistics Lecture Notes - Monograph Series

An adaptive significance threshold criterion for massive multiple hypotheses testing

Cheng Cheng

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This research deals with massive multiple hypothesis testing. First regarding multiple tests as an estimation problem under a proper population model, an error measurement called Erroneous Rejection Ratio (ERR) is introduced and related to the False Discovery Rate (FDR). ERR is an error measurement similar in spirit to FDR, and it greatly simplifies the analytical study of error properties of multiple test procedures. Next an improved estimator of the proportion of true null hypotheses and a data adaptive significance threshold criterion are developed. Some asymptotic error properties of the significant threshold criterion is established in terms of ERR under distributional assumptions widely satisfied in recent applications. A simulation study provides clear evidence that the proposed estimator of the proportion of true null hypotheses outperforms the existing estimators of this important parameter in massive multiple tests. Both analytical and simulation studies indicate that the proposed significance threshold criterion can provide a reasonable balance between the amounts of false positive and false negative errors, thereby complementing and extending the various FDR control procedures. S-plus/R code is available from the author upon request.

Chapter information

Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 51-76

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing 62F05: Asymptotic properties of tests 62F07: Ranking and selection 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions 62G05: Estimation 62E99: None of the above, but in this section
Secondary: 62E10: Characterization and structure theory 62E17: Approximations to distributions (nonasymptotic) 60E15: Inequalities; stochastic orderings

multiple tests false discovery rate $q$-value significance threshold selection profile information criterion microarray gene expression

Copyright © 2006, Institute of Mathematical Statistics


Cheng, Cheng. An adaptive significance threshold criterion for massive multiple hypotheses testing. Optimality, 51--76, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000392.

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