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Empirical Bayes Control of the False Discovery Exceedance

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Abstract

In sparse large-scale testing problems where the false discovery proportion (FDP) is highly variable, the false discovery exceedance (FDX) provides a valuable alternative to the widely used false discovery rate (FDR). We develop an empirical Bayes approach to controlling the FDX. We show that for independent hypotheses from a two-group model and dependent hypotheses from a Gaussian model fulfilling the exchangeability condition, an oracle decision rule based on ranking and thresholding the local false discovery rate (lfdr) is optimal in the sense that the power is maximized subject to FDX constraint. We propose a data-driven FDX procedure that emulates the oracle via carefully designed computational shortcuts. We investigate the empirical performance of the proposed method using simulations and illustrate the merits of FDX control through an application for identifying abnormal stock trading strategies.

Suggested Citation

  • Pallavi Basu & Luella Fu & Alessio Saretto & Wenguang Sun, 2021. "Empirical Bayes Control of the False Discovery Exceedance," Working Papers 2115, Federal Reserve Bank of Dallas.
    • Handle: RePEc:fip:feddwp:93384
    DOI: 10.24149/wp2115
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    More about this item

    Keywords

    Cautious Data Mining; False Discovery Exceedance Control; Local False Discovery Rates; Multiple Hypotheses Testing; Poisson Binomial Distribution; Trading Strategies;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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