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

研究了无外变量的多变量方法中的变量选择问题，特别是主成分分析中的变量选择问题。在本研究中，我们讨论了以下几个方面。在前人的研究中，我们详细介绍了Tanaka&Mori的方法(改进的主成分分析)和一些新的主成分分析中的变量选择方法。也就是说，我们提出了四种分步选择程序，并对它们进行了评估，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和确定选择的变量数量。我们采用了敏感性分析的思想作为选择变量的新标准。在敏感性分析方面，我们开发了统计软件包SAMMIF，它不仅可以方便地检测单个观测数据，还可以检测联合影响观测数据。利用这一思想，我们提出了一种新的选择方法，找到一个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。并开发了用于主成分分析变量选择的软件VASPCA。这是一个包括所有选择方法的交互软件，有两种类型的版本，用于Windows的VASPCA/Win和用于互联网的VASPCA/Web。

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.