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...

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Bibliographic Details
Published in:Econometrica 2021-01, Vol.89 (1), p.475-506
Main Authors: Mu, Xiaosheng, Pomatto, Luciano, Strack, Philipp, Tamuz, Omer
Format: Article
Language:English
Subjects:
Comparison of experiments
Data processing
divergences
Dominance
Inequality
Measurement
stochastic dominance
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Summary: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.
ISSN:0012-9682
1468-0262
DOI:10.3982/ECTA17548