| Project/Area Number |
17K05373
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Tahata Kouji 東京理科大学, 理工学部情報科学科, 准教授 (30453814)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 離散多変量解析 / 分割表解析 / スパース推定 / モデル選択 / 情報理論的アプローチ / 正方分割表解析 / スパース分割表 / パラメータ推定と検定 |
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| Outline of Final Research Achievements |
Various types of asymmetry models are proposed for the analysis of square contingency tables with ordinal categories. In this research, an asymmetry model family is given and models included in it are referred to as nonhierarchical models. Thus, we treat a problem of model selection because it is not easy to compare two models. For the problem, we employ the penalized likelihood approach and the simulation studies are given. Also, we show that each of asymmetry models can be interpreted as a property that it is the closest to the symmetry model in terms of the Kullback-Leibler divergence under some conditions. Moreover, we consider a model that indicates the structure of asymmetry for cell probabilities for square contingency tables. The model is the closest to the symmetry model in terms of the f-divergence under certain conditions and incorporates existing asymmetry models in special cases.
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| Academic Significance and Societal Importance of the Research Achievements |
同じ分類からなる正方分割表データは、医学・薬学、政治学、心理学など量的に測ることのできない変量を扱う分野に現れる。分割表解析の大きな関心は、分類間の独立性であるが、同じ分類からなる正方分割表では、多くの場合に独立性は成り立たない。したがって、対称性の解析を行うことが多い。研究成果は、幅広い非対称性のモデルからデータに対して適切なモデルを自動的に判断することを可能にした。このことにより、専門的な知識のない一般ユーザにとって、対称性を用いたデータ解析が身近なものとなったと考える。
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