2001 Fiscal Year Final Research Report Summary
Research on order restricted parameters and information criteria
| Project/Area Number |
11680331
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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 |
Statistical science
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| Research Institution | Seinan Gakuin University |
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Principal Investigator |
ANRAKU Kazuo Department of Literature, Seinan Gakuin University, Professor, 文学部, 教授 (90184332)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUCHI Yasuki School of Health Science, Nagasaki University, Associate Professor, 医学部, 助教授 (10124140)
NOMAKUCHI Kentarou Faculty of Science, Kochi University, Professor, 理学部, 教授 (60124806)
HIRAO Kojima Department of Commerce, Seinan Gakuin University, Professor, 商学部, 教授 (80170249)
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| Project Period (FY) |
1999 – 2001
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| Keywords | information criterion / AIC / Kullback-Leibler information / order restriction / bootstrap / change point / convexity / Monte Carlo simulation |
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| Research Abstract |
The summary of research results is as follows :
(a) We assume independent random samples from several populations whose corresponding parameters satisfy certain ordered relation. Under this assumption, we considered and investigated an information criteria based on the Kullback-Leibler information, as with the Akaike's Information Criterion (AIC). Especially, focusing on the bias-correction term and the asymptotic properties for some specific exponential family of distributions, we drove a specific formula for it, which indicates that the bias-correction term depends on the unknown parameters contrary to the ordinal AIC.
(b) Based on the above consideration, the bootstrap method has been developed for estimating the bias-correction term. Moreover, it was compared with the AlC-based method by Kikuchi and Yanagawa (1993) and MDL criterion on a Monte Carlo simulation study, assuming normal distributions for the population distributions.
(c) For some special cases of normal distributions as the population distributions, we gave an unbiased estimator for the bias-correction term.
(d) From the graphical convexity of the maximum likelihood estimators, through the pool adjacent violators algorithm (PAVA) under an order restriction, we have shown the bootstrap maximum likelihood estimators yield further biases, compared to the maximum likelihood estimators.
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Research Products
(20 results)
