Influence diagnostics in statistical data analysis

(1)在主成分分析(PCA)和典型相关分析中导出了Cook的局部影响，其中感兴趣的参数不包含在似然函数中，而包含在约束中，并且证明了其结果与影响函数的主成分分析(以V的g-逆为其度量)的结果是等价的，后者是我们用于多情况诊断的一般方法。(Tanaka等人，Comm.统计学家，A，2002；张、田中，《日本日报》。SoC。公司。张和田中在《环境科学与技术学院杂志》2002年的《一般统计建模》和《主成分分析》中详细讨论了库克的局部影响和我们的多病例诊断的一般方法之间的关系。统计学家。2003年的数据分析。我们的方法对Cook从几何角度引入的思想提供了良好的统计解释，并且我们的方法具有易于扩展到除极大似然情况以外的情况并且易于健壮的优点。(3)在泛函PCA中发展了一种影响分析方法，并被《计算统计》(Yamanishi和Tanaka)接受发表。它的数学方面在即将发表在田中(2004)的JAP年鉴上的手稿中进行了详细的讨论。SoC。公司。统计一下。(4)在比例风险模型中提出了一种多病例诊断方法，并在横滨举行的国际统计建模会议上作了介绍(Sung和Tanaka，2003)。全文将发表在2004年的《计算机科学与技术学报》上(Sung和Tanaka，2004)，并对所提方法的性能进行了数值研究(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方法(Morita和Tanaka，J.Jap)。SoC。公司。统计学家，2003年)。

(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).