Statistical Inference on cross sectionally contoured distributions

横截面轮廓分布的统计推断

• 批准号: 10680313
• 负责人: TAKEMURA Akimichi
• 金额: $ 1.92万
• 依托单位: The 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680313/
• 关键词: multivariate analysis; invariance; Gaussian process; 星形分布; 主成分分析; 判別分析

In this research we have obtained some important results concerning the theory of cross sectionally contoured distributions and related problems of statistical inference. Takemura and Kamiya have separately published a survey papers (in Japanese) in Proceedings of the Institute of Statistical Mathematics, Vol. 47, No. 1 (1999).Takemura with coauthor Satoshi Kuriki gives a survey on the tube method and the Euler characteristic method for obtaining the tail probability of the maximum of Gaussian field. This methodology is a topic of intense current research. Kamiya has developed a characterization of invariant probability models based on the functional form of the density function.Some other results include the discussion paper by Kamiya and Takemura :"Rankings generated by spherical discriminant analysis", Discussion Paper CIRJE-F-15, Faculty of Economics, Univ. of Tokyo (1998), which is going to appear in the Journal of the Japan Statistical Society.Takemura with coauthor Kuriki published a paper on principal component analysis in Communications in Statistics.

在这项研究中，我们获得了一些重要的结果，横截面轮廓分布理论和相关的统计推断问题。Takemura和Kamiya分别在Proceedings of the Institute of Statistical Mathematics，Vol.47，No.1（1999）上发表了一篇综述性论文（日文），Takemura与合著者Satoshi Kuriki综述了求高斯场最大值尾概率的管方法和欧拉特征线方法。这种方法是当前研究的热点。神谷研究了基于密度函数的函数形式的不变概率模型的特征。其他成果包括神谷和武村的讨论论文：“Rankings generated by spherical discriminant analysis”，Discussion Paper CIRJE-F-15，Faculty of Economics，Univ. of Tokyo（1998），这篇论文将发表在Journal of the Japan Statistical Society上。武村与合著者栗木在Communications in Statistics上发表了一篇关于主成分分析的论文。

项目成果

Satoshi Kuriki and Akimichi Takemura: "Distribution of the maximum of Gaussian random field : tube method and Euler characteristic method. (in Japanese)"Proceedings of the Institute of Statistical Mathematics. Vol. 47. 201-221 (1999)

Satoshi Kuriki 和 Akimichi Takemura：“高斯随机场最大值的分布：管法和欧拉特征法。（日语）”统计数学研究所论文集。

紙屋英彦: "不変確率モデルの特徴付け"統計数理. 47・1. 63-69 (1999)

神谷秀彦：“不变概率模型的表征”统计数学 47・1（1999）。

Hidehiko Kamiya and Akimichi Takemura: "Rankings generated by spherical discriminant analysis"Journal of the Japan Statistical Society. (印刷中).

Hidehiko Kamiya 和 Akimichi Takemura：“通过球形判别分析生成的排名”日本统计学会杂志（正在出版）。

Akimichi Takemura and Satoshi Kuriki: "Shrinkage to smooth non-convex cone : principal component analysis as Stein estimation"Commun. Statist. - Theory Meth.. Vol. 28. 651-669 (1999)

Akimichi Takemura 和 Satoshi Kuriki：“平滑非凸锥体的收缩：斯坦因估计的主成分分析”Commun。

Kamiya,H.and Eguchi,S.: "A class of robust principal component vectors" Research Memorandum No.699 Institute of Statistical Mathematics October. (1998)

Kamiya,H. 和 Eguchi,S.：“一类稳健主成分向量”研究备忘录第 699 号统计数学研究所 10 月。