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）和规范相关分析中得出的，其中感兴趣的参数不包含在可能性函数中，而是包含在约束中，并且结果表明结果等于PCA的结果。（以V为v的G-Inverse）影响功能，我们将其用作多案例诊断的一般方法。（Tanaka等人，Comm。Statist。，A，2002; Zhang and Tanaka，Jap。Soc。Comp。Comp。Statist。，2002）（2）Cook的本地影响与我们的多用期诊断方法之间的关系张和田中在一般统计建模中讨论了《环境科学与技术学院杂志》，2002年，详细介绍了塔纳卡等人的详细信息。统计学家。 2003年的数据分析。我们的方法为库克的想法提供了一种合理的统计解释，从几何学的角度引入，我们的方法具有优势，即可以轻松地扩展到除最大可能性的情况以外的其他情况下，并且可以轻松地将其扩展（3）在功能性PCA中开发了一种影响分析的方法，并接受了计算统计（Yamanishi和Tanaka）的出版物。它的数学方面在田中（2004年）的《 JAP年鉴》（2004年）中的手稿中进行了详细讨论。 Soc。 comp。统计（田中）。（4）提出了一种以比例危害模型提出的多案例诊断方法，并在横滨举行的国际统计模型会议上提出（Sung and Tanaka，2003年）。完整的论文将出现在Compstat2004的论文集（Sung and Tanaka，2004年），并进行了数值研究以研究拟议方法的性能（Sung and Tanaka，J。环境科学技术学院）。（5）A影响分析方法是在潜在类别分析中提出的（Morita和Tanaka，J。Jap。Soc。Comp。Comp。Statist。，2003）。