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Abstract:
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In this talk, we address two important challenges of large-scale multiple testing: (i) strong dependence between test statistics and (ii) heavy tailedness of the data. We employ a multi-factor structure model to characterize the dependence, and propose a Huber loss based approach to construct test statistics for testing individual hypotheses. Our procedure asymptotically controls the overall false discovery proportion at the nominal level under mild conditions. Numerical studies on both simulated and real data sets are carried out to support our theory. It is shown that the robust, covariate-adjusted method significantly outperforms the multiple t-tests under strong dependence, and is applicable even when the true error distribution deviates wildly from the normal distribution.
A key technical tool in our analysis is a nonasymptotic Bahadur representation for Huber's robust M-estimator in the presence of heavy-tailed errors. Specifically, we develop an exponential-type concentration inequality, which yields a number of important Gaussian approximation results that may be of independent interest.
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