Hidetoshi Murakami

Correlation analysis of principal components from two populations

We investigate a correlation coefficient of principal components from two sets of variables. Using perturbation expansion, we get a limiting distribution of the correlation. In addition, we obtain a limiting distribution of the Fishers z transformation of the above correlation. Additionally, we verify the accuracy of the limiting distributions using Monte Carlo simulations. Finally in this study, we present two examples and a bootstrap estimation.

Saddlepoint Approximations to the Limiting Distribution of the Modified Anderson-Darling Test Statistic

The approximation for the distribution function of test statistic is extremely important in statistics. The standard and higher-order saddlepoint approximations are considered in tails of the limiting distribution for the modified Anderson–Darling test. The saddlepoint approximations are compared with the approximation of Sinclair et al. (1990) for upper tail area. An empirical function is derived to estimate the critical values of a saddlepoint approximation.

A Multisample Rank Test for Location-Scale Parameters

One of the multisample problems is discussed in this article. A new multisample rank tests based on a k-sample Baumgartner statistic are proposed for testing the location-scale parameters. The exact critical values of proposed statistics are calculated. Simulations are used to investigate the power of proposed statistics for various population distributions.

Permutation Test for Equality of Individual an Eigenvalue from a Covariance Matrix in High-Dimension

A test statistic for examining the equality of an individual eigenvalue in two populations of high dimension is proposed. The asymptotic distribution of the proposed statistic is derived and the validity of the permutation test is discussed. Simulations were used to investigate the power of the suggested statistic. The proposed statistic is applied to hand measurement data on white and aboriginal Australians to test the equality of the eigenvalues.

Power Comparison of Multivariate Wilcoxon-type Tests Based on the Jurečková–Kalina’s Ranks of Distances

A multivariate two-sample testing problem is one of the most important topics in nonparametric statistics. One of the multivariate two-sample testing problems based on the Jurečková–Kalina ranks of distance is discussed in this article. Further, a multivariate Wilcoxon-type test is proposed for testing the equality of two continuous distribution functions. Simulations are used to investigate the power of this test for the two-sided alternative with various population distributions. The results show that the proposed test statistic is more suitable than various existing statistics for testing a shift in the locationt and location-scale parameters.

Model based on skew normal distribution for square contingency tables with ordinal categories

For the analysis of square contingency tables with ordinal categories, Tahata, Yamamoto and Tomizawa (2009) considered the normal distribution type symmetry model, which may be appropriate if it is reasonable to assume an underlying bivariate normal distribution with equal marginal variances. The present paper proposes a new model which may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate skew normal distribution with equal marginal variances. Simulations are used to investigate the fitting of new model for bivariate skew normal distribution. The decayed teeth data are analyzed by using the new model.