Study of variable selection methods integrated in data analysis and development of interactive system for variable selection

本文主要研究无外部变量的多元分析方法中的变量选择问题，特别是在主成分分析（PCA）中。在本研究中，我们讨论了以下内容。在前人的研究中，我们详细地考虑了Tanaka & Mori的方法（修正PCA）以及PCA中一些新的变量选择方法。即提出了四种逐步选择程序并对其进行了评价，并对其标准进行了数值研究。我们将计算机密集型方法（Bootstrap和交叉验证技术）应用于选择结果，然后可以获得信息来评估方法并确定要选择的变量数量。我们采用敏感性分析的思想作为选择变量的新准则。在敏感性分析方面，我们开发了SAMMIF统计包，既可以方便地检测单个影响观测值，也可以方便地检测联合影响观测值。利用这一思想，我们提出了一种新的选择方法，即找到对主成分分析结果或参数估计影响最小的变量，然后将其删除。我们还开发了用于主成分分析中变量选择的VASPCA软件。这是一个交互式软件，包括所有的选择方法，并有两种类型的版本，VASPCA/Win为Windows和VASPCA/Web为互联网。

We study variable selection in multivariate methods without external variables, especially in principal component analysis (PCA). In this study we discuss the followings.1. We consider Tanaka & Mori's method (Modified PCA) in detail among the previous studies and some new methods for variable selection in PCA. That is, we propose four stepwise selection procedures and evaluate them, and investigate its criteria numerically.2. We apply the computer intensive methods (Bootstrap and Cross-validation techniques) to the results of the selection and then can obtain information to evaluate the methods and to determine the number of variables to be selected.3. We adopt the idea of sensitivity analysis as a new criterion to select variables. As for sensitivity analysis, we develop the statistical package "SAMMIF" which can be used conveniently for detecting not only singly but also jointly influential observation. Using the idea we propose a new selection method to find a variable which has the smallest influence on the result or parameter estimations of PCA and then delete it.4. We also develop the software "VASPCA" for variable selection in PCA. This is an interactive software which includes all the selection methods and has two types of versions, VASPCA/Win for Windows and VASPCA/Web for the internet.