| Project/Area Number |
16500168
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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 | Kagoshima University (2006)
Obihiro University of Agriculture and Veterinary Medicine (2004-2005) |
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Principal Investigator |
TANNICHI Nobuhiro Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (00207200)
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| Co-Investigator(Kenkyū-buntansha) |
SEKIYA Yuri Hokkaido University of Education, Faculty of Education, Professor, 教育学部, 教授 (10226665)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | full multnomial model / product multinomial model / independent null hypothesis / homogeneity / asymptotic expansion / local alternative / non-local alternative / improved transformation / 分割表 / 漸近展開 / φ-ダイバージェンス / パワーダイバージェンス / 改良変換統計量 / 局所エッジワース展開 / モンテカルロ法 / φ-ダイバージェンス統計量 / パワーダイバージェンス統計量 / フルマルチノミアル / 離散項 / 積多項モデル |
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| Research Abstract |
1. In the case that r X s contingency table is considered as full multinomial model, we derive expression of asymptotic expansion for the distribution of the test statistics based on Φ-divergence under independent null hypothesis. The expression consists of continuous and discontinuous terms. Evaluation for the continuous and discontinuous term is also considered. Using the term of asymptotic expansion assuming a continuous distribution in the expression, we construct transformation for improving small-sample accuracy of chi-square approximation of the distribution of the statistic under independent hypothesis.
2. In the case that r X s contingency table is considered as product multinomial model, we derive expression of asymptotic expansion for the distribution of the test statistics based on power-divergence under null hypothesis that all of the multinomial populations are homogeneity. The expression consists of continuous and discontinuous terms. Evaluation for the continuous and discontinuous term is also considered when the number of samples from each population is the same.
3. In the test of independence in full multinomial model, by assuming the continuity of the random variables, we derive asymptotic expansions for the distribution of the test statistics based on power-divergence under local alternative and non-local alternative hypotheses, respectively.
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