2001 Fiscal Year Final Research Report Summary
Theory of Bayes interence and its applications
| Project/Area Number |
12640131
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kumamoto University |
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Principal Investigator |
TAKADA Yoshikazu Kumamoto University, Faculty of Engineering, Professor, 工学部, 教授 (70114098)
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| Co-Investigator(Kenkyū-buntansha) |
IWASA Manabu Kumamoto University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30232648)
NAITO Koichiro Kumamoto University, Faculty of Engineering, Professor, 工学部, 教授 (10164104)
OSHIMA Yoichi Kumamoto University, Faculty of Engineering, Professor, 工学部, 教授 (20040404)
KUDOTA Noriya Kumamoto University, Faculty of Engineering, Lecturer, 工学部, 講師 (80185884)
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| Project Period (FY) |
2000 – 2001
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| Keywords | LINEX loss function / Bayes sequential estimation / asymptotic efficiency / inadmissibility |
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| Research Abstract |
There are some cases for which it is appropriate to use asymmetric loss function instead of symmetric loss function, Throughout this research project, we used LINEX loss function proposed by Varian (1975). In 2000, consideration was devoted to the sequential point estimation of normal mean, Purely and accelerated stopping times were considered. It was shown that a sequential procedure with the sample mean as an estimate is asymptotically inadmissible. Furthermore, we considered a sequential point estimation of the mean vector of a multivariate normal distribution. It was also shown that a sequential procedure with the sample mean vector as an estimate is asymptotically inadmissible.
In 2001, we considered Bayes sequential estimation of the mean of one- parameter exponential family with conjugate priors. It is extremely difficult to find Bayes stopping times. Hence we considered APO rules proposed by Bickel and Yahav (1967) to find asymptotic optimal stopping times. Especially, it was shown that the APO rules is asymptotically second-order efficient compared with Bayes rule for a Poisson distribution. In the future research project, we shall consider whether the similar result holds for one-parameter exponential family. Furthermore, on the basis of obtained results, we are going to consider empirical Bayes sequential estimation.
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