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Generalized α-investing: definitions, optimality results and application to public databases

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  • Ehud Aharoni
  • Saharon Rosset

Abstract

type="main" xml:id="rssb12048-abs-0001"> The increasing prevalence and utility of large public databases necessitates the development of appropriate methods for controlling false discovery. Motivated by this challenge, we discuss the generic problem of testing a possibly infinite stream of null hypotheses. In this context, Foster and Stine suggested a novel method named α-investing for controlling a false discovery measure known as mFDR. We develop a more general procedure for controlling mFDR, of which α-investing is a special case. We show that, in common practical situations, the general procedure can be optimized to produce an expected reward optimal version, which is more powerful than α-investing. We then present the concept of quality preserving databases which was originally introduced by Aharoni and co-workers, which formalizes efficient public database management to save costs and to control false discovery simultaneously. We show how one variant of generalized α-investing can be used to control mFDR in a quality preserving database and to lead to significant reduction in costs compared with naive approaches for controlling the familywise error rate implemented by Aharoni and co-workers.

Suggested Citation

  • Ehud Aharoni & Saharon Rosset, 2014. "Generalized α-investing: definitions, optimality results and application to public databases," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 771-794, September.
  • Handle: RePEc:bla:jorssb:v:76:y:2014:i:4:p:771-794
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.76.issue-4
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    Cited by:

    1. Max Grazier G'Sell & Stefan Wager & Alexandra Chouldechova & Robert Tibshirani, 2016. "Sequential selection procedures and false discovery rate control," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 423-444, March.
    2. Shiyun Chen & Ery Arias-Castro, 2021. "On the power of some sequential multiple testing procedures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 311-336, April.
    3. Hahn, Georg, 2022. "Online multivariate changepoint detection with type I error control and constant time/memory updates per series," Statistics & Probability Letters, Elsevier, vol. 181(C).
    4. Genoni, Giulia & Quatto, Piero & Vacca, Gianmarco, 2023. "Dating financial bubbles via online multiple testing procedures," Finance Research Letters, Elsevier, vol. 58(PA).
    5. Gong, Siliang & Zhang, Kai & Liu, Yufeng, 2018. "Efficient test-based variable selection for high-dimensional linear models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 17-31.

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