TY - JOUR
AU1 - Kolotilin, Anton
AU2 - Wolitzky, Alexander
AB - 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.
TI - Distributions of posterior quantiles via matching
JF - Theoretical Economics
DO - 10.3982/te6057
DA - 2024-11-01
UR - https://www.deepdyve.com/lp/wiley/distributions-of-posterior-quantiles-via-matching-oqjhr2bSLs
SP - 1399
EP - 1413
VL - 19
IS - 4
DP - DeepDyve
ER -