The purpose of this paper is to develop a nonparametric k-sample test based on a modified Baumgartner statistic. We define a new modified Baumgartner statistic B* and give some critical values. Then we compare the power of the B* statistic with the t-test, the Wilcoxon test, the Kolmogorov-Smirnov test, the Cramér-von Mises test, the Anderson-Darling test and the original Baumgartner statistic. The B* statistic is more suitable than the Baumgartner statistic for the location parameter when the sample sizes are not equal. Also, the B* statistic has almost the same power as the Wilcoxon test for location parameter. For scale parameter, the power of the B* statistic is more efficient than the Cramér-von Mises test and the Anderson-Darling test when the sizes are equal. The power of the B* statistic is higher than the Kolmogorov-Smirnov test for location and scale parameters. Then the B* statistic is generalized from two-sample to k-sample problems. The B*_k statistic denotes a k-sample statistic based on the B* statistic. We compare the power of the B*_k statistic with the Kruskal-Wallis test, the k-sample Kolmogorov-Smirnov test, the k-sample Cramér-von Mises test, the k-sample Anderson-Darling test and the k-sample Baumgartner statistic. Finally, we investigate the behavior of power about the B*_k statistics by simulation studies. As a result, we obtain that the B*_k statistic is more suitable than the other statistics.

View full abstract

This article focuses on a new characteristic quantity, “similarity distance”, which is defined for a pair of time series data and reflects similarity between them. This characteristic quantity is defined with the help of a smooth approximating function, which is obtained by “WISAM (Wavelet Interpolation Method with Simulated Annealing)” developed by Mori (1999) and Mori and Misawa (2001). Afterwards, as an illustrated example of the usage of similarity distance together with WISAM, the classifications and similarity of the annual GDP data for ten regions in Japan are investigated.

View full abstract

Ranked preference data arise in the situation that a large number of people (voters) rank several objects (candidates) in order of their extent of preference, for instance, multiple voting with ranking or a questionnaire of preference ranking. Such data are supposed to include the information about similarity among candidates in the sense that those who are highly preferred by the same voter would seem to be similar to the voter. Based on this idea, we have proposed a method to evaluate the geometrical configuration and distance between candidates by applying multidimensional scaling (MDS) on ranked preference data in which each voter votes multiple candidates consistently with their preference ranking. In this paper, we have an experiment in order to investigate the feasibility of this method. Using simulative data, we examine whether our method can retrieve the original configuration. We generate candidates and voters simulatively and apply this method to the data obtained. We also have an application to actual data obtained from students about allocation to advisory professor at undergraduate course (for bachelor degree).

View full abstract

Discussion is made upon numerical computation for the distributions of the smallest and the largest latent roots of Wishart random matrices by numerically evaluating the series in zonal polynomials of high degree. Graphs for bivariate to quadrivariate distributions of the smallest latent root and for trivariate ones of the latter are shown for several values of parameters.

View full abstract

For fitting any theoretical model, we introduce the Power Transform-Both-sides (PTB) approach and the Power Transform-Both-sides and Weighted Least Squares (PTBWLS) approach which implements a power weighted transformation approach in PTB. Then, as an alternative to the PTB, we provide a Nonparametric Transform-Both-sides (NTB) approach to express function transformation as a cubic spline curve. As an estimation method which combines PTBWLS with together NTB, we propose a Nonparametric Transform-Both-sides and Weighted Least Squares (NTBWLS) approach. Through the numerical investigation of one example using data generated from a 1-compartment model, we conclude that PTB and PTBWLS induce normally distributed additive errors and stabilize the error variance, and NTBWLS improves the degrees of normality and homoscedasticity of the error more than PTB and PTBWLS.

View full abstract

For square contingency tables with ordered categories, the marginal homogeneity (MH) model is equivalent to the equality of row and column marginal ridits. This paper proposes a measure to represent what degree the row marginal ridit departs from the column marginal ridit. The measure is expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index, which is applied to the marginal ridits. It is useful for comparing the degree of departure from MH in several tables. Examples are given. The proposed measure is also compared with the measure of departure from MH by Tahata, Iwashita and Tomizawa (2006), and with the goodness-of-fit test statistic of the MH model.

View full abstract