From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again

Xiaosheng Mu, Luciano Pomatto, Philipp Strack, Omer Tamuz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Rényi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Rényi divergences.

Original languageEnglish (US)
Pages (from-to)475-506
Number of pages32
JournalEconometrica
Volume89
Issue number1
DOIs
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Keywords

  • Comparison of experiments
  • divergences
  • stochastic dominance

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