Large-scale multiple testing of composite null hypotheses under heteroskedasticity.

The article focuses on addressing methodological challenges in simultaneous multiple testing of composite null hypotheses under heteroskedasticity, where the variance of test statistics varies and may be correlated with the parameter of interest. It proposes a heteroskedasticity-adjusted multiple testing (HAMT) procedure that avoids standardization of test statistics and instead incorporates variance information directly via an improved nonparametric empirical Bayes deconvolution estimator. Theoretical results establish that HAMT asymptotically controls the false discovery rate (FDR) and achieves optimal power comparable to an oracle procedure with full knowledge of the data-generating process. Extensive simulations demonstrate that HAMT outperforms existing methods, particularly when the parameter and variance are dependent, and the approach is illustrated with applications including mobile app user engagement detection.