TY - GEN

T1 - Asymptotics of Bayesian estimation for nested models under misspecification

AU - Miya, Nozomi

AU - Suko, Tota

AU - Yasuda, Goki

AU - Matsushima, Toshiyasu

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84873564746&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:84873564746

SN - 9784885522673

T3 - 2012 International Symposium on Information Theory and Its Applications, ISITA 2012

SP - 86

EP - 90

BT - 2012 International Symposium on Information Theory and Its Applications, ISITA 2012

T2 - 2012 International Symposium on Information Theory and Its Applications, ISITA 2012

Y2 - 28 October 2012 through 31 October 2012

ER -