Sensitivity Analysis in Complex Statistical Models

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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 data-sets 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].