| Project/Area Number |
09640280
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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 | Kumamoto University |
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Principal Investigator |
YOKOYAMA Takahisa Faculty of Engineering, Assistant Prof., 工学部, 講師 (20240864)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Takashi Okayama University of Science, Faculty of Informatics, Prof., 総合情報学部, 教授 (20069074)
TAKADA Yoshikazu Faculty of Science, Associates Prof., 理学部, 助教授 (70114098)
SAKATA Toshio Faculty of Engineering, Associates Prof., 工学部, 助教授 (20117352)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Repeated Measures / Random Effects / Covariance Structure / Growth Curve Model |
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| Research Abstract |
First we propose test statistics for a general hypothesis concerning the adequacy of multivariate random-effects covariance structures in a multivariate growth curve model with differing numbers of random effects. Since the exact likelihood ratio (LR) statistic for the hypothesis is complicated, it is suggested to use a modified LR statistic. An asymptotic expansion of the null distribution of the statistic is obtained. The exact LR statistic is also discussed (Yokoyama, T., J.Statist. Plann. inference 65 (1997) 281 -292). Next we consider profile analysis in two extended growth curve models. The first is a growth curve model with parallel mean profiles, which has a random-effects covariance structure based on a single response variable ; the second is a multivariate growth curve model with parallel mean profiles, which has a multivariate random-effects covariance structure based on several response variables. For testing "no condition variation" and "level" hypotheses concerning parallel mean profiles of several groups, we obtain the criteria proposed by Wald along with their asymptotic null distributions. We give a numerical example of these asymptotic results (Yokoyama, T., Hiroshima Math. J.28 (1998) 345 - 354).
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