2012 Fiscal Year Final Research Report
New development of statistical estimation of parameters with linear inequalities restriction
| Project/Area Number |
22500263
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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 | Mejiro University |
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Principal Investigator |
WATANABE Genso (張 元宗) 目白大学, 社会学部, 教授 (40227343)
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| Co-Investigator(Kenkyū-buntansha) |
SHINOZAKI Nobuo 慶應義塾大学, 名誉教授 (70051886)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 統計的推測 |
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| Research Abstract |
We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959).Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in terms of estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is also discussed.We also discuss the above problems under Pitman closeness criterion and confirm the validity of Pitman closeness criterion.
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