From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again.
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 sample...
| Published in: | Econometrica Vol. 89; no. 1; pp. 475 - 507 |
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| Main Authors: | , , , |
| Format: | Article |
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Wiley-Blackwell
Jan2021
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=148146686&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 148146686 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00129682 ECN jtl: Econometrica issn: 00129682 maglogo: Y pubinfo: dt: Jan2021 vid: 89 iid: 1 pid: 480 pub: Wiley-Blackwell artinfo: ui: 148146686 10.3982/ECTA17548 ppf: 475 ppct: 32 formats: tig: atl: From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again. aug: au: Mu, Xiaosheng Pomatto, Luciano Strack, Philipp Tamuz, Omer affil: Department of Economics, Princeton University Division of the Humanities and Social Sciences, Caltech Department of Economics, Yale University su: Social dominance Electronic data processing Stochastic dominance Integral inequalities sug: subj: Social dominance Electronic data processing Data Processing, Hosting, and Related Services Stochastic dominance Integral inequalities keyword: Comparison of experiments divergences stochastic dominance Comparison of experiments divergences stochastic dominance ab: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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