Project/Area Number  08680331 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Statistical science

Research Institution  Okayama University 
Principal Investigator 
TANAKA Yutaka Okayama University, Dept.of Environmental & Mathematical Sciences, Professor, 環境理工学部, 教授 (20127567)

CoInvestigator(Kenkyūbuntansha) 
ODAKA Yoshimasa Kurashiki University of Science and the Arts Dept.of Computer Science and Mathem, 産業科学技術学部, 教授 (50109740)
KURIHARA Koji Okayama University, Dept.of Environmental & Mathematical Sciences, Assoc.Profess, 環境理工学部, 助教授 (20170087)
TARUMI Tomoyuki Okayama University, Dept.of Environmental & Mathematical Sciences, Professor, 環境理工学部, 教授 (50033915)

Project Fiscal Year 
1996 – 1997

Project Status 
Completed(Fiscal Year 1997)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1996 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Sensitivity analysis / Influential observations / Influence functions / Influenctial subsets / Local influence / Multivariate analysis / Influence function / Influential subsets / sensitivity analysis / influence function / local influence / multivariate methods / covariance structure analysis 
Research Abstract 
In these two years we put emphasis on the studies of the following topics : 1) Relationship between two approaches to sensitivity analysis (SA), one based on influence functions and the other based on Cook's local influence and its applications, 2) SA in multivariate methods of incomplete data, 3) Development of principal component analysis based on a subset of variables and its SA,4) Development of unified software for SA in various multivariate methods. For the first topic we have studied covariance structure analysis (CSA), which includes many kinds of multivariate methods. We have considered four cases defined by {CSA without/with functional constraints} x {we are interested in all/a subset of parameters}, and have found that in all cases both approaches provide essentially equivalent results, if we introduce the same perturbation to the maximum likelihood estimation of normal theory CSA.On the basis of this equivalence we can develop SA which can be applied to detect jointly as well as singly influential observations ( [6], TR [2]). For the second topic we have developed SA procedure in multivariate analyzes of datasets containing socalled ignorable missing values by applying the implicit function theorem to the EM algorithm of estimating the means and covariances ( [8], [10]). For the third and fourth topics see [3], [9] & [11].
