OPTIMAL RATES OF CONVERGENCE FOR ESTIMATING THENULL DENSITY AND PROPORTION OF NONNULL EFFECTS INLARGE-SCALE MULTIPLE TESTING

摘要

An important estimation problem that is closely related to large-scalemultiple testing is that of estimating the null density and the proportion ofnonnull effects. A few estimators have been introduced in the literature; how-ever, several important problems, including the evaluation of the minimaxrate of convergence and the construction of rate-optimal estimators, remainopen.