Alfredo Di Tillio (IGIER - Università Bocconi)

This paper develops a framework to evaluate the impact of sample selection on the quality of statistical inference. An evaluator tests a hypothesis based on observation of a sample selected as the most favorable of several observations. The impact of this sample selection on the evaluator’s payoff is characterized through a generalization of Lehmann’s comparison of location experiments. The evaluator benefits from greater selection when the data distribution’s quantile density function is less elastic than in Gumbel’s extreme value distribution. The evaluator is harmed either when the data distribution has sufficiently thick tails and the hypothesis would be rejected at the prior, or when tails are sufficiently thin and the prior is to accept the hypothesis.

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