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Article type: Cover
2005 Volume 17 Issue 2 Pages
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Article type: Cover
2005 Volume 17 Issue 2 Pages
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Article type: Appendix
2005 Volume 17 Issue 2 Pages
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Article type: Index
2005 Volume 17 Issue 2 Pages
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Article type: Index
2005 Volume 17 Issue 2 Pages
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Tomohiro Nakamura, Hideyuki Douke
Article type: Article
2005 Volume 17 Issue 2 Pages
75-85
Published: August 31, 2005
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When we recognize a significance difference between two population mean vectors by the statistical test, it is often necessary to investigate whether the variates in all variates have the significance difference. In this study, we partition all variates into several partial variates and consider the group sequential procedure to test sequentially the difference between two partial population mean vectors corresponding to each group of partial variates. Then we propose two group sequential procedures based on the statistic by using the design matrix and based on the Rao's statistic. In the simulation, we calculate the repeated confidence boundaries based on two statistics when we change the number of all variates and the number of the group of partial variates. Furthermore we compare the power of the test on two group sequential procedures. In a case study, we apply two group sequential procedures to the significance test after partitioning several groups of partial variates based on weather data of two cities.
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Toshio Shimokawa, Masashi Goto
Article type: Article
2005 Volume 17 Issue 2 Pages
87-108
Published: August 31, 2005
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In the fields of physical, medical and social sciences, multivariate analysis of large scale data, especially discriminant analysis has been often applied. Ordinary discriminant analyses (such as, linear or quadratic discriminant analyses) are usually based on the multivariate normality of observations. However, the observations obtained in practice rarely satisfy this constrained assumption. Thus, in order to satisfy the multivariate normality of the observations, methods using multivariate normalizing transformation of the observations are presented. However, in the methods depending on the framework of such a "transformation" we cannot choose a suitable transformation when we discriminate the newly obtained observations. As a substitutional approach, we can consider this discriminant problem on the basis of the framework of "multivariate distribution" corresponding to the transformation. Then, we propose the methodology of the data-adaptive discriminant analysis (DDA), assuming the multivariate power-normal distribution as the underlying distribution of the observations, where the multivariate power-normal distribution is defined as the distribution specified before the multivariate power transformation. By DDA, we can assess the appropriateness of the linear or quadratic discriminant analyses since the multivariate power-normal distribution includes the multivariate normal distribution. Moreover, we present some diagnostic methods to DDA, and evaluate the performance of the data-adaptive discriminant analysis by certain literature examples and simulations. As a result, the data-adaptive discriminant analysis has better performance than other discrimination techniques based on multivariate normal distribution.
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Hideaki Hida
Article type: Article
2005 Volume 17 Issue 2 Pages
109-125
Published: August 31, 2005
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The paper proposes a new procedure to detect interaction and outliers with nonparametric regression model that cannot directly express interaction by itself. In other words, based on the residuals from fitting Generalized Additive Model (GAM) to the data with interaction, systematic inadequacy is regarded as interaction. Along with the idea mentioned above, the procedure to detect interaction and outliers graphically and numerically is proposed. The outline of the procedure is as follows. Fit GAM to the data, and then stratify the observations with respect to the value(s) of the explanatory variable(s). And when the tendency of the residual plots differs between the strata, it's concerned that the data contain interaction. Furthermore, with respect to the statistics evaluating the difference of tendency between the strata, the hypothesis of "no interaction" or "no local data structure" can be examined. From the simulation study, when the tendency of the residual plots differs between the strata, it was confirmed that the data contain interaction. And, when the clear-cut difference cannot be seen in the residual plots between strata, it was confirmed that the data don't contain interaction. Finally, it was shown that the test could judge the existence of interaction adequately. Besides, it's confirmed that local interactions, outliers and global interactions can be detected essentially in the same manner.
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Kimitoshi Ikeda, Tomoyuki Sugimoto, Masashi Goto
Article type: Article
2005 Volume 17 Issue 2 Pages
127-146
Published: August 31, 2005
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The conventional methods for analysis of longitudinal data are not flexible enough for exploring the nonlinear underlying data structures. But interactions among time and other covariates exist in many longitudinal data, the way of evaluation of the interactions will show the superiority or inferiority of the analysis methods. Furthermore, time trend of observations has nonlinear structure in many cases, describing this structure is connected with describing the mean structure of observations correctly. In this paper, as a convenient method to explore the nonlinear structure and, especially, interactions structure in longitudinal data, we focus on Multivariate Adaptive Regression Splines (MARS). And we present MARS for analysis of longitudinal data (L-MARS), and we demonstrate the methodology. Moreover, we evaluate the trial performance through case examination and the simulation.
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Mika Sato
Article type: Article
2005 Volume 17 Issue 2 Pages
147-156
Published: August 31, 2005
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Conventionally, fuzzy multivariate data analysis has been proposed along with the issue of positively introducing uncertainty in real data and the methodology itself. Fuzzy Clustering is one method which can capture the uncertainty situation of real data and it is well known that fuzzy clustering can obtain a robust result as compared with conventional hard clustering. Following along with the emphasis on the general problem of data analysis, which is a solution for analyzing a huge amount of complex data, the merit of fuzzy clustering for this is expected. In this paper, we describe fuzzy clustering methods, which are methods in fuzzy multivariate analysis, along with several hybrid methods of fuzzy clustering and conventional multivariate analysis which have recently been proposed by us based on the idea that the multiple merits of methods can cope with the inherent classification structures.
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[in Japanese], [in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
157-
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[in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
157-
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[in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
157-
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[in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
158-
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[in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
158-
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Article type: Article
2005 Volume 17 Issue 2 Pages
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[in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
158-
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Article type: Article
2005 Volume 17 Issue 2 Pages
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Article type: Article
2005 Volume 17 Issue 2 Pages
159-
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Article type: Article
2005 Volume 17 Issue 2 Pages
159-
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[in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
159-
Published: August 31, 2005
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Article type: Article
2005 Volume 17 Issue 2 Pages
159-
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[in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
159-
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Article type: Article
2005 Volume 17 Issue 2 Pages
160-
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Article type: Article
2005 Volume 17 Issue 2 Pages
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Article type: Article
2005 Volume 17 Issue 2 Pages
160-
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[in Japanese], [in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
160-
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Article type: Article
2005 Volume 17 Issue 2 Pages
160-161
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Article type: Article
2005 Volume 17 Issue 2 Pages
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Article type: Article
2005 Volume 17 Issue 2 Pages
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Article type: Article
2005 Volume 17 Issue 2 Pages
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2005 Volume 17 Issue 2 Pages
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2005 Volume 17 Issue 2 Pages
162-
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2005 Volume 17 Issue 2 Pages
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Article type: Article
2005 Volume 17 Issue 2 Pages
162-
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2005 Volume 17 Issue 2 Pages
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2005 Volume 17 Issue 2 Pages
163-
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Article type: Article
2005 Volume 17 Issue 2 Pages
163-
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Article type: Article
2005 Volume 17 Issue 2 Pages
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2005 Volume 17 Issue 2 Pages
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2005 Volume 17 Issue 2 Pages
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Article type: Article
2005 Volume 17 Issue 2 Pages
164-
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Article type: Article
2005 Volume 17 Issue 2 Pages
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[in Japanese], [in Japanese], [in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
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[in Japanese], [in Japanese], [in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
165-
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Article type: Article
2005 Volume 17 Issue 2 Pages
165-
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[in Japanese], [in Japanese], [in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
165-
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Article type: Article
2005 Volume 17 Issue 2 Pages
165-
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Article type: Article
2005 Volume 17 Issue 2 Pages
166-
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[in Japanese], [in Japanese]
Article type: Article
2005 Volume 17 Issue 2 Pages
166-
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