FROM BLACKWELL DOMINANCE IN LARGE SAMPLES TO RENYI DIVERGENCES AND BACK AGAIN
成果类型：
Article
署名作者：
Mu, Xiaosheng; Pomatto, Luciano; Strack, Philipp; Tamuz, Omer
署名单位：
Princeton University; California Institute of Technology; Yale University
刊物名称：
ECONOMETRICA
ISSN/ISSBN：
0012-9682
DOI：
10.3982/ECTA17548
发表日期：
2021
页码：
475-506
关键词：
摘要：
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 Renyi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Renyi 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 Renyi divergences.