Decision theoretic approach to computer intensive methods of multivariate analysis

多变量分析计算机密集方法的决策理论方法

• 批准号: 08680327
• 负责人: TAKEMURA Akimichi
• 金额: $ 1.54万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08680327/
• 关键词: Asymptotic expansion; shrinkage; Likelihood Ratio; MANOVA; Bartlett correction; Heteroscedasticity; Shrinkage estimator

First we summarize research results by the head investigator Akimichi Takemura. He has published with the co-author Satoshi Kuriki the paper "A proof of independent Bartlett correctability of nested likelihood ratio tests" in Annals of Institute of Statistical Mathematics. This paper proves that the likelihood ratio statistics for nested hypotheses can be Bartlett-corrected independently of each other. His paper with the co-author Toshio Honda "The effect of heteroscedasticity on the actual size of Chow test" appeared in Journal of the Japan Statistical Society. In this paper he has obtained results on the actual signigicance levels of the test of structural change (Chow test), when the error terms of the regression model has heteroscedasticity. His paper with Hidehiko Kamiya titled "On rankings generated by pairwise linear discriminant analysis of m populations" appeated in the Journal of Multivariate Analysis. This paper investigates the number of rankings and properties of non-appearing rankings in detail based on the theory of hyperplane arrangements. His most recent publication "Weights of chi distribution for smooth or piecewise smooth cone alternattives. The annals of statistics" in the Annals of Statistics investigates the weights of chi-bar-squared distribution for smooth convex cone alternatives using differential geometric methods.Next we summarize research results by Tatsuya Kubokawa. His paper with M.S.Srivastava titled "Double shrinkage estimators of ratio of variances" appeared in the Proceedings of the Sixth Eugene Lukacs Symposium. This paper gives a new shrinkage estimator for the ratio of variances. Furthermore "Shrinkage estimators in a mixed MANOVA and GMANOVA model" by Y.Kubokawa, and A.K.Md.E.Saleh compares shrinkage estimators in Multivariate Analysis Variance Model and its generalizations.

首先，我们总结了首席研究员竹村明美的研究成果。他与合著者栗木聪在《统计数学研究所年鉴》上发表了论文《嵌套似然比检验的独立Bartlett可校正性证明》。本文证明了嵌套假设的似然比统计量可以相互独立地进行Bartlett校正。他与合著者本田俊夫的论文《异方差对周检验实际大小的影响》发表在《日本统计学会杂志》上。本文在回归模型误差项具有异方差的情况下，得到了结构变化检验(Chow检验)的实际显著水平的结果。他与神谷英彦的论文题为《关于m个人口的成对线性判别分析产生的排名》，发表在《多元分析杂志》上。本文以超平面排列理论为基础，详细研究了非出现排序的个数和性质。他最近在《统计年鉴》上发表的文章《光滑或分段光滑锥交替的卡方分布的权重.统计年鉴》用微分几何方法研究了光滑凸锥备选的卡方分布的权重。下面我们总结久保川的研究结果。他与斯里瓦斯塔瓦共同撰写的题为《方差比的双收缩估计器》的论文发表在第六届尤金·卢卡奇研讨会论文集上。本文给出了方差比的一种新的收缩估计。此外，Y.Kubokawa和A.K.M.E.Saleh在《混合Manova和GMANOVA模型中的收缩估计》中比较了多元分析方差模型及其推广中的收缩估计。

项目成果

Akimichi Takemura and Satoshi Kuriki: "A proof of independent Bartlett correctability of nested likelihood ratio tests" Annals of Institute of Statistical Mathematics. 48. 603-620 (1996)

Akimichi Takemura 和 Satoshi Kuriki：“嵌套似然比检验的独立 Bartlett 可校正性的证明”统计数学研究所年鉴。

Y.konno, T.Kubokawa and A.K.Md.E.Saleh: ""Shrinkage estimators in a mixed MANOVA and GMANOVA model."" Statistics and Decisions. Vol.15. 37-49 (1997)

Y.konno、T.Kubokawa 和 A.K.Md.E.Saleh：“混合 MANOVA 和 GMANOVA 模型中的收缩估计器。”统计和决策。

Akimichi Takemura and Satoshi Kuriki: "Weights of chi2 distribution for smooth or piecewise smooth cone alternatives" The annals of Statistics. 25. (1997)

Akimichi Takemura 和 Satoshi Kuriki：“平滑或分段平滑圆锥替代方案的 chi2 分布权重”统计年鉴。

Akimichi Takemura and Hidehiko Kamiya: "On rankings generated by pairwise linear discrlminant analysis of m populations" Journal of Multivariate Analysis. 61. 1-28 (1997)

Akimichi Takemura 和 Hidehiko Kamiya：“关于 m 个群体的成对线性判别分析生成的排名”多元分析杂志。

Akimichi Takemura and Toshio Honda: "The effect of heteroscedasticity on the actual size of Chow test" Journal of the Japan Statistical Society. 26. 127-134 (1996)

Akimichi Takemura 和 Toshio Honda：“异方差性对 Chow 检验实际大小的影响”日本统计学会杂志。