Bulletin of the Computational Statistics of Japan

Varimax rotation is often used in factor analysis in order to make the interpretation of the loading matrix easy to understand by trying to reduce it into a simple structure. In this paper the author applies the rotation to canonical discriminant analysis for the same purpose, replacing the loading matrix by the canonical variates standardized in terms of the within-group variance. The method is illustrated by two data sets: medical data on the aged with 9 groups, 62 individuals and 16 variables, and Fisher's iris data. A set of simple artificial data is also presented in order to make it easier to understand the method and to check the correctness of the computer program.

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Andersen (1992) proposed an index that evaluates the influence of each cell on the parameter estimates for the parametric multinomial distribution. The index is the analogue of Cook's distance (Cook & Weisberg, 1982). However, it is difficult to explain the meaning of the index from a point of view of a statistical model, because the index is constructed from an estimator based on a conditional distribution that there is no observation in a cell. Therefore, in this paper we propose an index that is meaningful from a view point of a statistical model. Furthermore, we derive the one step approximation of the index.

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In principal component analysis, a latent vector of a covariance matrix is important for interpreting a principal component. So we consider the hypothesis testing which is an quality between the α-th largest latent vector and the specified vector. In this paper we propose two new test statistics and derive the asymptotic expansion of the distributions under the null hypothesis, though we know well the statistic given by T. W. Anderson. We obtain the power of tests using three statistics under various alternative hypotheses by a simulation study, and compare the power of tests using them. Our results show that the new statistics are superior to the statistic of Anderson in some ranges of alternative hypotheses.

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The 9th symposium of the Japanese Society of Computational Statistics was held at Ryogoku in Tokyo from 19th Oct. 1995. Special theme was "The past, present and future of statistical software package in Japan". The following two sessions were attempted to discuss about historical aspects. One was a history of statistical software in Japan present by three special guests and the other was a history of SAS and SPSS in Japan presented by two special guests. Three sessions were aimed for the present of statistical software in Japan. Those are as follows: First session is about foreign statistical software such as SAS, SPSS, Statistica and S. Second session is about domestic software such as StatPartner, JUSE-QCAS and EXCEL Taikou. Third session is about Mathematica, Mathcad and two free softwares developed by universities. The one session was about statistical education. We discussed what we shall do from now. In this paper, the first part introduces why special theme is chosen, the second part is the summary of 19 papeers of the symposium and third one is what we should do after the symposium.

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