Estimating the false discovery rate using the stochastic approximation algorithm

Testing of multiple hypotheses involves statistics that are strongly dependent in some applications,

but most work on this subject is based on the assumption of independence. We propose

a new method for estimating the false discovery rate of multiple hypothesis tests, in which the

density of test scores is estimated parametrically by minimizing the Kullback–Leibler distance

between the unknown density and its estimator using the stochastic approximation algorithm,

and the false discovery rate is estimated using the ensemble averaging method. Our method is

applicable under general dependence between test statistics. Numerical comparisons between our

method and several competitors, conducted on simulated and real data examples, show that our

method achieves more accurate control of the false discovery rate in almost all scenarios.