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**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.

### MSC:

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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\textit{C. C. Heyde} and \textit{K. Au}, J. Stat. Theory Pract. 2, No. 2, 221--232 (2008; Zbl 1427.62005)

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### References:

[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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