Tetsuto Himeno

Seismic Wave Interactions Between the Atmosphere - Ocean - Cryosphere System and the Geosphere in Polar Regions

At the time of the International Geophysical Year (IGY; 1957-1958), it was generally understood by a majority of seismologists that no extreme earthquakes occurred in polar regions, particularly around Antarctica. Despite the Antarctic being classified as an aseismic region, several significant earthquakes do occur both on the continent and in the surrounding oceans. Since IGY, an increasing number of seismic stations have been installed in the polar regions, and operate as part of the global network. The density of both permanent stations and temporary deployments has improved over time, and has recently permitted detailed studies of local seismicity (Kaminuma, 2000; Reading, 2002; 2006; Kanao et al., 2006).

Testing homogeneity of mean vectors under heteroscedasticity in high-dimension

This paper is concerned with the problem of testing the homogeneity of mean vectors. The testing problem is without assuming common covariance matrix. We proposed a testing statistic based on the variation matrix due to the hypothesis and the unbiased estimator of the covariance matrix. The limiting null and non-null distributions are derived as each sample size and the dimensionality go to infinity together under a general population distribution, which includes elliptical distribution with finite fourth moments or distribution assumed in Chen and Qin (2010). In two-sample case, our proposed test has the same asymptotic power as Chen and Qin (2010)s test. In addition, it is found that our proposed test has the same asymptotic power as the one of Dempsters trace statistic for MANOVA proposed in Fujikoshi et?al. (2004) for the case that the population distributions are multivariate normal with common covariance matrix for all groups. A small scale simulation study is performed to compare the actual error probability of the first kind with the nominal.

Interval estimation in discriminant analysis for large dimension

ABSTRACT This paper is concerned with the interval estimation for the log odds of the posterior probability that the observation vector belongs to one of two homoscedastic multivariate normal distributions (Π1 and Π2). We give the limiting distribution of the unbiased estimator for the log odds as the sample sizes and the dimension jointly tend to infinity, and approximate the confidence interval based on the asymptotic distribution. Small-scale simulations are performed to check the precision of the approximation.