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Influence diagnostics in statistical data analysis

统计数据分析中的影响诊断

基本信息

批准号：
13680374
负责人：
TANAKA Yutaka
金额：
$ 1.79万
依托单位：
Okayama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13680374/
关键词：
influence analysis sensitivity analysis local influence influence function principal component analysis multiple-case diagnostics robust diagnostics functional data analysis canonical correlation canonical correlations

项目摘要

(1) Cook's local influence is derived in principal component analysis (PCA) and canonical correlation analysis, where the parameters of interest are not contained in the likelihood function but contained in constraints, and it is shown that the results are equivalent to those of PCA (with g-inverse of V as its metric) of influence functions, which we use as a general method of multiple-case diagnostics. (Tanaka et al., Comm. Statist., A, 2002; Zhang and Tanaka, Annals of Jap. Soc. Comp. Statist., 2002)(2) The relationship between Cook's local influence and our general method of multiple-case diagnostics is discussed in general statistical modeling by Zhang and Tanaka in Journal of the Faculty of Environmental Science & Technology, 2002, and in PCA in details Tanaka et al., Comp. Statist. Data Analysis in 2003. Our method provides a sound statistical interpretation for Cook's idea which is introduced from geometrical point of view, and our method has advantages that it can be extended easily to the cases other than the case of maximum likelihood and that it can easily be robustified.(3) A method of influence analysis is developed in functional PCA and it was accepted for publication in Computational Statistics (Yamanishi and Tanaka). Its mathematical aspect is discussed in details in a manuscript to be published in Tanaka(2004), Annals of Jap. Soc. Comp. Stat. (Tanaka).(4) A method of multiple-case diagnostics is proposed in proportional hazard models and is presented in an international meeting on Statistical Modeling held at Yokohama (Sung and Tanaka, 2003). The full paper will appear in Proceedings of COMPSTAT2004 (Sung and Tanaka,2004) and a numerical study is carried out to study the performance of the proposed method (Sung and Tanaka, J. Faculty of Environmental Science & Technology).(5) A method of influence analysis is proposed in latent class analysis (Morita and Tanaka, J. Jap. Soc. Comp. Statist., 2003).

(1)库克的局部影响是在主成分分析（PCA）和典型相关分析中推导出来的，其中感兴趣的参数不包含在似然函数中，而是包含在约束中，并且结果与影响函数的PCA（以V的g逆作为其度量）的结果是等效的，我们将其用作多情况诊断的一般方法。（Tanaka等人，通讯员，A，2002; Zhang和Tanaka，Annals of Japan. Soc. Comp. Statistist.，2002）（2）Cook的局部影响与我们的多案例诊断的一般方法之间的关系在Zhang和Tanaka在Journal of the Faculty of Environmental Science & Technology，2002中的一般统计建模中进行了讨论，并在Tanaka等人的PCA中进行了详细讨论。Comp. Statist. 2003年数据分析。我们的方法提供了一个健全的统计解释库克的想法，这是从几何的角度来看，我们的方法具有的优点，它可以很容易地扩展到其他情况下比最大似然的情况下，它可以很容易地被robustified。(3)在功能PCA中开发了一种影响分析方法，并在计算统计学（Yamanishi和Tanaka）上发表。它的数学方面在田中（2004），日本社会统计年鉴（Annals of Japan. Soc. Comp. Stat.）（田中）。(4)在比例风险模型中提出了一种多情况诊断方法，并在横滨举行的统计建模国际会议上提出（Sung和Tanaka，2003）。全文将出现在COMPSTAT 2004会议录（Sung和Tanaka，2004年）和数值研究进行了研究所提出的方法的性能（Sung和Tanaka，J.环境科学与技术学院）。(5)在潜在类别分析中提出了一种影响分析的方法（Morita和Tanaka，J. Jap. Soc. Comp. Statist，2003年）。