A Cautionary Note on Model Choice and the Kullback-Leibler Information
The Kullback-Leibler information has found application in many areas of statistical science. It typically arises in model choice and model dimension questions in a way which suggests its use as a distance. Indeed, it has been widely described as a distance although it comprehensively fails to be a metric. Some pitfalls in interpreting it as a distance are discussed and, in particular, its application to discriminate between prospective risky asset returns distributions.
Key-wordsDiscrimination Entropy Heavy-tailed Statistical distance
AMS Subject Classification62G32 62P05 94A17
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