### Abstract

We analyze the asymptotic properties of the cumulative logarithmic loss in the decision problem based on the Bayesian principle and explicitly identify the constant terms of the asymptotic equations as in the case of previous studies by Clarke and Barron and Gotoh et al. We assume that the set of models is given that identify a class of parameterized distributions, it has a nested structure and the source distribution is not contained in all the families of parameterized distributions that are identified by each model. The cumulative logarithmic loss is the sum of the logarithmic loss functions for each time decision -, e.g., the redundancy in the universal noiseless source coding.

Original language | English |
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Title of host publication | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 |

Pages | 86-90 |

Number of pages | 5 |

Publication status | Published - 2012 Dec 1 |

Event | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 - Honolulu, HI, United States Duration: 2012 Oct 28 → 2012 Oct 31 |

### Publication series

Name | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 |
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### Conference

Conference | 2012 International Symposium on Information Theory and Its Applications, ISITA 2012 |
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Country | United States |

City | Honolulu, HI |

Period | 12/10/28 → 12/10/31 |

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

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## Cite this

*2012 International Symposium on Information Theory and Its Applications, ISITA 2012*(pp. 86-90). [6401057] (2012 International Symposium on Information Theory and Its Applications, ISITA 2012).