2015 Fiscal Year Final Research Report
The mathematical theory of statistical multiple comparisons
| Project/Area Number |
24540148
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 | Nanzan University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 多重比較検定法 / 閉検定手順 / 同時信頼区間 / 分布論 / 数値解析 |
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| Outline of Final Research Achievements |
We derived the following conclusions (i)-(iv) for multiple comparison procedures in multi-sample models. (i) Suppose that the simple order restriction of means is satisfied under the underlying normal distribution. Then, for the differences among mean responses, a closed testing procedure is superior to the single step Hayter's test (Hayter (1990)). To compute the upper percentiles of the distributions of statistics, the sinc method described in Lund and Bowers (1992) and Stenger (1993) is utilized. (ii) Suppose that the underlying distribution is a normal distribution function with unequal variances. Then, for the differences among mean responses, Shiraishi and Hayakawa (2015) propose a closed testing procedure superior to the single step Games-Howell test. (iii) Suppose that the underlying distribution is unknown. Then nonparametric multiple comparison procedures are discussed. (iv) Under Bernoulli distribution, the theory of multiple comparison procedures are constructed.
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| Free Research Field |
数理統計学
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