Distributions of posterior quantiles via matching

• 成果类型: Article
• 署名作者: Kolotilin, Anton; Wolitzky, Alexander
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE6057
• 发表日期: 2024-11-01
• 页码: 1399-1413
• 关键词: Quantiles; statistical experiments; median matching; overconfidence; gerrymandering; persuasion; C61; D72; D82

摘要

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 is an element of (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.