论文信息 - On Estimating Many Means, Selection Bias, and the Bootstrap

On Estimating Many Means, Selection Bias, and the Bootstrap

AbstractWithrecentadvancesinhighthroughputtechnology,researchersoftenﬁndthemselvesrunningalargenumberofhypothesistests(thousands+)andesti-matinga largenumber ofeﬀect-sizes. Generallythereis particular interest inthose eﬀects estimated to be most extreme. Unfortunately naive estimates oftheseeﬀect-sizes(evenafterpotentiallyaccountingformultiplicityinatestingprocedure)canbeseverelybiased. Inthismanuscriptweexplorethisbiasfromafrequentistperspective: wegiveaformaldeﬁnition,andshowthatanoracleestimator using this bias dominates the naive maximum likelihood estimate.We give a resampling estimator to approximate this oracle, and show that itworkswellonsimulateddata. WealsoconnectthistoideasinempiricalBayes.Keywords: bootstrap, shrinkage, mean, empirical Bayes, James-Stein, regres-siontothemean,selectionbias,compounddecisiontheory 1 Introduction Often, in modern applications, researchers are interested in testing and estimatingeﬀectsizesformanydiﬀerentfeaturesatonce. Inthesimplestcasesoneisinterested

Noah Simon | Richard Simon | N. Simon | R. Simon

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