2006 Fiscal Year Final Research Report Summary
Exploratory statistical theory after searching the underlying distribution
| Project/Area Number |
16540112
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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 | Yokohama-City University |
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Principal Investigator |
SHIRAISHI Takaaki Yokohama-City University, International College of Arts and Sciences, Professor, 国際総合科学部, 教授 (50143160)
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| Co-Investigator(Kenkyū-buntansha) |
KONNO Yoshihiko Japan Women's University, Department of Mathematical and Physical Sciences, Faculty of Science, Professor, 理学部, 教授 (00205577)
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| Project Period (FY) |
2004 – 2006
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| Keywords | robust statistics / asymptotic theory / computational simulation / multiple comparisons / algorithm / nonparametorics |
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| Research Abstract |
1. As statistical estimation procedures for location, the sample mean, Hodges and Lehman's R-estimator, and Huber's M-estimator are introduced in a one-sample model. The asymptotic distributional theory for the three estimators and simulated mean squared errors give the features of the respective estimators depending on the underlying distribution. Based on the features, we propose an estimation procedure selecting one of the three estimators after searching a distribution near to the underlying distribution. It is shown that the mean squared error of the new estimator is more stable than the three estimators. Next, as distribution-free test procedures, the conditional t-test, Wilcoxon's signed rank test, and the M-test are introduced. Asymptotic relative efficiency and simulated power of the respective tests are investigated. Based on their features, we propose a stable test procedure selecting one of the three tests after searching a distribution near to the underlying distribution.
2
… More
. In a one-way analysis of variance model, robust versions based on scale-invariant M-statistics are proposed for single-step multiple comparisons procedures discussed by Tukey (1953), Dunnett (1955), and Scheffe (1953). Although the distributions for the normal theory pocedures are given by double integrals, the asymptotic distributions for the proposed procedures are expressed as single integrals. Tables of asymptotic critical values are provided for the proposed M procedures. Furthermore although the symmetry of the underlying distribution is needed in the asymptotic theory of Huber's M-estimators, the proposed procedures do not demand the symmetry. It is found that the M-procedures are superior to the classical normal theory procedures except the case that an underlying distribution is normal.
3. In the one-way layout assuming that the underlying distribution is normal, we may execute Tukey-Kramer multiple comparisons procedure for searching all pairwise differences of locations. For the unequal sample sizes, the Tukey-Kramer (T-K) method is conservative. The T-K method is given by using the upper c point of the studentized range distribution A(t). A(t) is a lower bound for the distribution of the Tukey-Kramer statistic. We derive the distribution B(t) which gives an upper bound for the distribution of Tukey-Kramer statistic. By using numerical double integration, we show that the value of B(t) is a little larger than that of A(t). As the result, we may verify that the conservativeness of the T-K method is small. Less
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Research Products
(15 results)
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[Book] 統計データ科学事典2007
Author(s)
杉山高一等編集, 白石高章1部執筆
Total Pages
18
Publisher
朝倉書店
Description
「研究成果報告書概要(和文)」より
