A cautionary note on model choice and the Kullback-Leibler information. (English) Zbl 1427.62005

Summary: 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.


62B10 Statistical aspects of information-theoretic topics
62G32 Statistics of extreme values; tail inference
62P05 Applications of statistics to actuarial sciences and financial mathematics
94A17 Measures of information, entropy
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[1] Gani, J.; Seneta, E., Stochastic Methods and their Applications: Papers in honour of Chris Heyde (2004)
[2] Glasserman, P.; Kou, S., A conversation with Chris Heyde, Statistical Science, 21, 286-298 (2006) · Zbl 1333.01042
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