Sensitivity analysis and variable selection in statistical models

统计模型中的敏感性分析和变量选择

基本信息

批准号：
16500175
负责人：
TANAKA Yutaka
金额：
$ 1.92万
依托单位：
Nanzan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16500175/
关键词：
Sensitivity analysis Influence analysis Statistical diagnostics Kernel method Functional data analysis Variable selection Proportional hazards model diagnostics spatial prediction robust influence analysis influence sensitivity ker

项目摘要

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

1。内核多变量方法中的灵敏度分析（SA）：我们在内核PCA中提供了一种SA的方法。并提出了一种可能在生物系统中发挥重要作用的可能性（参见Yamanishi，Y。＆Tanaka，2006; Tanaka＆Yamanishi，2006年）。 . is 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在功能性ra中，我们发现库克的d可以表达大约为……更多的残留和杠杆功能，就像普通ra一样（Harasawa，Fueda＆Tanaka，2006）3。我们得出了与Cox的分数危害模型有关绑定的观察结果并提出了一种不包括唱歌的SA，而是多案例诊断（Sung＆Tanaka，2004年），我们对我们的方法进行了有用性。研究并显示了我们的一般稳健SA支撑的联合应用（1994年）和Atkinson's为方法提供了精确的观察信息A＆Nakaya，2006年）。它用于空间预测，并研究了其将其应用于数值示例（Choi，Beum＆Tanaka，2006年）。6。 PCA我们发现了基于Tanaka＆Mori（1997）结构的程序比其他方法更好（Mori等，2005，2007）。