Research on Sensitivity Analysis in Multivariate Methods

在这两年中，我们在多变量方法的敏感性分析中重点研究了以下四个主题：1)通过消除所谓的掩蔽效应来检测影响子集的实用方法，2)基于变量子集的PCA敏感性分析程序的开发，3)偏最小二乘回归分析（PLS）敏感性分析程序的开发，以及4)用于多变量方法敏感性分析的统计软件。对于第一个主题，我们在COMPESTAT'94论文中提出了一个稳健的敏感性分析程序，并在Tanaka（1994）和北京ISI的一个专题贡献论文会议上讨论了我们的程序与Cook的本地影响方法之间的关系。关于第二个主题，我们已经在1995年汉城ICSQP会议上发表的一篇特邀论文以及田中和森的论文中进行了充分讨论，该论文将发表在《美国数学与管理科学杂志》上。对于第三个主题，我们推导了PLS中的影响函数，并提出了一种敏感性分析程序的方法。在1994年第五届日中统计研讨会上发表之后，我们现在正在撰写关于这一主题的论文全文。作为统计软件，我们发表了SACS/B (Watadani and Tanaka, 1994)，它不仅可以单独检测，也可以联合检测协方差结构分析中的有影响的观测值，包括验证性因子分析、探索性因子分析和LISREL模型。

In these two years we focused on the following four topics in sensitivity analysis in multivariate methods : 1) Practical methods for detecting influential subsets by eliminating the so-called masking effect, 2) Development of a sensitivity analysis procedure in PCA bsed on a subset of variables, 3) Development of a sensitivity analysis procedure in partial least squares regression analysis (PLS) , and 4) Statistical software for sensitivity analysis in multivariate methods. For the first topic we proposed a robust sensitivity analysis procedure in COMPESTAT'94 paper, and also discussed the relationship between our procedure and Cook's local influence approach in Tanaka (1994) and in the presentation in a selected topic contributed paper session in ISI,Beijing. Concerning the second topic we have fully discussed in an invited paper presented in ICSQP'95 at Seoul and in Tanaka and Mori's paper which will appear in American Journal of Mathematical and Management Sciences. For the third topic we have derived influence functions in PLS and proposed a method of sensitivity analysis procedure. After presented in the fifth Japan-China Symposium on Statistics in 1994 we are now writing a full paper on this topic. As statistical software we have published SACS/B (Watadani and Tanaka, 1994) , which can detect not only singly but also jointly influential observations in covariance structure analysis including confirmatory factor analysis, exploratory factor analysis and LISREL models.