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2013

On Estimating Many Means, Selection Bias, and the Bootstrap

Simon, Noah, Simon, Richard

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With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes.

Generally there is particular interest in those effects estimated to be most extreme.
Unfortunately naive estimates of these effect-sizes (even after potentially accounting for multiplicity in a testing procedure) can be severely biased.
In this manuscript we explore this bias from a frequentist perspective: we give a formal definition, and show that an oracle estimator using this bias dominates the naive maximum likelihood estimate.

On Estimating Many Means, Selection Bias, and the Bootstrap · Around

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Asymptotically subminimax solutions of compound statistical decision problems
H. Robbins · 1956
Earlier work this paper cites.
Inadmissibility of the usual estimator for the mean of a multivariate normal distribution
C. Stein · 1956
Earlier work this paper cites.
Estimation with quadratic loss
W. James and C. Stein · 1961
Earlier work this paper cites.
Stein’s estimation rule and its competitors – an empirical bayes approach
B. Efron and C. Morris · 1973
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