Influence diagnostics in statistical data analysis

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(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).