Sensitivity analysis and variable selection in statistical models

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1. Sensitivity analysis (SA) in kernel multivariate methods : We proposed a method of SA in kernel PCA. Basic idea is to approximate the transformed Hilbert space defined by the kernel function with finite dimensional Euclidean space and apply our general procedure of SA in ordinary multivariate methods. We applied our method to metabolic gene network data and suggested a possibility of finding genes which played important role in the biological system (see, Yamanishi, Y. ＆ Tanaka, 2006; Tanaka ＆ Yamanishi, 2006). The same idea can be used for developing SA in kernel canonical correlation analysis (CCA).2. SA in functional data analysis : We proposed methods of sensitivity analysis in functional PCA, regression analysis (RA) and CCA. In SA in PCA we discussed the relation of our method with SA in ordinary PCA of the multivariate data obtained by sampling from the functional data (Yamanishi ＆ Tanaka, 2005). In SA in functional RA we found that Cook's D can be expressed approximately as … More a function of residuals and leverages as in the case of ordinary RA (Harasawa, Fueda ＆ Tanaka, 2006)3. SA in Cox's proportional hazards model : We derived influence functions related to Cox's proportional hazards models with tied observations and proposed a method of SA including not only single-case but also multiple-case diagnostics (Sung ＆ Tanaka, 2004). We showed usefulness of our method with the analysis of some numerical examples.4. Robust SA in factor analysis : We performed a simulation study and showed that joint application of our general method of robust SA proposed by Tanaka ＆ Watadani (1994) and Atkinson's forward search method provided precise information of the influence of observations (Yang, Tanaka ＆ Nakaya, 2006).5. We proposed a method of sensitivity analysis in covariogram model, which is used in spatial prediction, and studied its usefulness in applying it to a numerical example (Choi, Beum ＆ Tanaka, 2006).6. Variable selection in PCA and other multivariate methods without external variables : We performed comparative studies on the performances of various methods of variable selection in PCA, factor analysis and correspondence analysis. In PCA we found that the procedure based on Tanaka ＆ Mori (1997)'s modified PCA reveals the latent structure better than other methods (Mori et al., 2005, 2007). Less