| Project/Area Number |
11640128
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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 | Kagoshima University |
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Principal Investigator |
YAMATO Hajime Faculty of Science, Kagoshima University, Professor, 理学部, 教授 (90041227)
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| Co-Investigator(Kenkyū-buntansha) |
KONDO Masao Faculty of Science, Kagoshima University, Associate Professor, 理学部, 助教授 (70117505)
SAKAI Manabu Faculty of Science, Kagoshima University, Professor, 理学部, 教授 (60037281)
INADA Kouichi Faculty of Science, Kagoshima University, Professor, 理学部, 教授 (20018899)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1999: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Berry-Esseen Bound / Estimable parameter / Deficiency / Degree / Kernel / LB-statistic / U-statistic / V-statistic / ディリクレ過程 |
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| Research Abstract |
As estimators of estimable parameters, we consider three statistics which are U-statistic, V-statistic and limit of Bayes estimate. This limit of Bayes estimate, which we say LB-statistic, is obtained from Bayes estimate of estimable parameter based on Dirichlet process by letting its parameter tend to zero. For the estimable parameter with non-degenerate kernel, the asymptotic relative efficiencies of LB-statistic with respect to U-statistic and V-statistic, and that of V-statistic with respect to U-statistic are equal to one. To see difference between these three statistics, we evaluate deficiencies among LB-statistic, U-statistic and V-statistic.
With respect to the expression of LB-statistics with degenerate kernel as a linear combination of U-statistics, we show the properties of its components which are unbiasedness and degeneracy. Using these we give its asymptotic distribution. By the same methods, we show the asymptotic distribution of V-statistic with degenerate kernel. For the V-statistic, its asymptotic distribution is given by Borovskikh (1996 ), p.113, whose form and method are different from us. We confirm two are equivalent.
Associated with an estimable parameter, we consider a new class of statistics. It is described by a linear combination of U-statistics and includes V-statistic and LB-statistic as special cases. The kernel is assumed to be non-degenerate. For the difference between this linear combination and the well-known U-statistic, we derive upper bounds of its absolute moments about the origin and the mean. Using these upper bounds we show Berry-Esseen bound for the linear combination of U-statistics with exact expressions.
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