Bulletin of the Computational Statistics of Japan

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In this paper, we propose a new framework of statistical sensitivity analysis for linear discriminant analysis based on the sign of the influence function. In general, the average of discriminant scores and the misclassification rate based on cross-validation are important measures in discriminant analysis. However, when we perform statistical sensitivity analysis for a discriminant method, we often get different influential subsets for prediction accuracy and analysis result in the cases of the evaluation of individuals for the average of discriminant scores and the misclassification rate based on cross-validation. To deal with the above situation, we search a subset based on the common influential individuals in both cases, and regard the subset as a confidential influential subset. By investigating the characteristics of the individuals belonging to the common subset, we robustly perform statistical sensitivity analysis for the prediction accuracy in linear discriminant analysis. We apply our proposed approach to a two-discrimination problem in terms of a clinical side effect after thoracic endovascular aortic repair (TEVAR), and show the usefulness of our approach.

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This paper provides a formal asymptotic expansion of a sampling distribution of Generalized non-central F-statistic which is introduced by Fang and Zhang (1990, pp.86-88) and Mathai et al. (1995, p.99) under elliptical populations. In many cases, asymptotic expansions of distribution of non-central F-type statistic would be expressed by a weighted sum of non-central χ^2-distribution. For the generalized non-central F-statistic, however, the asymptotic expansion can be written in terms of non-central F-distribution. In the sequel, to evaluate the accuracy of the asymptotic expansion, we carry out some numerical experiments under typical elliptical distributions, namely, the normal distribution, the t-distribution and "ε-contaminated" normal distribution.

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In this paper, we propose a 'Bonsai' graph to represent the output of multiple regression analysis in graphical form. The BONSAI-SHAPED TREE graph is constructed the output of the multiple regression analysis by graphing R-squared as the stem thickness, the absolute values of the standard partial regression coefficient as the lengths of the branches, and the partial correlation coefficients as the angles of the branches. By graphing the results of the multiple regression analysis, we can easily determine visually the goodness of fit of the multiple regression equation, the degree of influence of the independent variable on the dependent variable, and the relationship between the independent variables.

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