Working Paper

Inference on winners

Authors

Adam McCloskey, Toru Kitagawa, Isaiah Andrews Adam McCloskey, Toru Kitagawa, Isaiah Andrews

Published Date

31 December 2018

Type

Working Paper (CWP73/18)

Many empirical questions can be cast as inference on a parameter selected through optimization. For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data. Such settings give rise to a winner’s curse, where conventional estimates are biased and conventional confidence intervals are unreliable. This paper develops optimal confidence sets and median-unbiased estimators that are valid conditional on the parameter selected and so overcome this winner’s curse. If one requires validity only on average over target parameters that might have been selected, we develop hybrid procedures that combine conditional and projection confidence sets to offer further performance gains relative to existing alternatives.


Previous version

Inference on winners
Adam McCloskey, Toru Kitagawa, Isaiah Andrews
CWP31/18