Distributions of posterior quantiles via matching

Anton Kolotilin and Alexander Wolitzky

Theoretical Economics, 2024, vol. 19, issue 4

Abstract: We offer a simple analysis of the problem of choosing a statistical experiment to optimize the induced distribution of posterior medians, or more generally q-quantiles for any q ∈ (0,1). We show that a single experiment---the q-quantile matching experiment---implements all implementable distributions of posterior q-quantiles, with different distributions spanned by different selections from the sets of posterior q-quantiles. A dense subset of implementable distributions of posterior q-quantiles can be uniquely implemented by perturbing the q-quantile matching experiment. A linear functional is optimized over distributions of posterior q-quantiles by taking the optimal selection from each set of posterior q-quantiles. The q-quantile matching experiment is the only experiment that simultaneously implements all implementable distributions of posterior q-quantiles.

Keywords: Quantiles; statistical experiments; overconfidence; gerrymandering; persuasion (search for similar items in EconPapers)
JEL-codes: C61 D72 D82 (search for similar items in EconPapers)
Date: 2024-11-14
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Related works:
Working Paper: Distributions of Posterior Quantiles via Matching (2024)
Working Paper: Distributions of Posterior Quantiles via Matching (2024)
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