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Simultaneous control of false positives and false negatives in multiple hypotheses testing

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  • Ebrahimi, Nader

Abstract

Multiple hypotheses testing is concerned with appropriately controlling the rate of false positives, false negatives or both when testing several hypotheses simultaneously. Nowadays, the common approach to testing multiple hypotheses calls for controlling the expected proportion of falsely rejected null hypotheses referred to as the false discovery rate (FDR) or suitable measures based on the positive false discovery rate (pFDR). In this paper, we consider the problem of determining levels that both false positives and false negatives can be controlled simultaneously. As our risk function, we use the expected value of the maximum between the proportions of false positives and false negatives, with the expectation being taken conditional on the event that at least one hypothesis is rejected and one is accepted, referred to as hybrid error rate (HER). We then develop, based on HER, an analog of p-value termed as h-value to test the individual hypotheses. The use of the new procedure is illustrated using the well-known public data set by Golub et al. [Molecular classification of cancer: class discovery and class prediction by gene expression monitoring, Science 386 (1999) 531-537] with Affymetrix arrays of patients with acute lymphoic leukemia and acute myeloid leukemia.

Suggested Citation

  • Ebrahimi, Nader, 2008. "Simultaneous control of false positives and false negatives in multiple hypotheses testing," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 437-450, March.
  • Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:437-450
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    References listed on IDEAS

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    1. Youngchao Ge & Sandrine Dudoit & Terence Speed, 2003. "Resampling-based multiple testing for microarray data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-77, June.
    2. Cohen, Arthur & Sackrowitz, Harold B., 2007. "More on the inadmissibility of step-up," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 481-492, March.
    3. Hall, Peter & Park, Byeong U., 2004. "Bandwidth choice for local polynomial estimation of smooth boundaries," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 240-261, November.
    4. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517.
    5. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498.
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