Yasunori Fujikoshi

A Generalized Tukey Conjecture for Multiple Comparisons among Mean Vectors

Abstract In this article the Tukey-Kramer procedure for multiple comparisons of pairwise differences of mean vectors in multivariate normal distributions is considered. A multivariate version of the Tukey-Kramer procedure is presented, and a generalized Tukey conjecture of the conservativeness of the simultaneous confidence intervals for all pairwise comparisons by this procedure is affirmatively proved in the case of three correlated mean vectors. Some properties of the multivariate Tukey-Kramer procedure are also presented, and simulation results for some selected parameters are given.

The effects on the distributions of sample canonical correlations under nonnormality

In this paper, we study the effects of nonnormality on the distributions of sample canonical correlations when the population canonical correlations are simple. In order to achieve the purpose, we derive asymptotic expansion formulas for the distributions of a function of the canonical correlations as well as the individual canonical correlations under nonnormal populations. We particularly discuss the distribution of sample canonical correlations under the class of elliptical population. These expansions are given by using a perturbation method. Simulation results are also given.

Tests for the mean direction of the Langevin distribution with large concentration parameter

In this paper we study the asymptotic behaviors of the likelihood ratio criterion (TL(s)), Watson statistic (TW(s)) and Rao statistic (TR(s)) for testing H0s: [mu] [set membership, variant] (a given subspace) against H1s: [mu] [negated set membership] , based on a sample of size n from a p-variate Langevin distribution Mp([mu], ?) when ? is large. For the case when ? is known, asymptotic expansions of the null and nonnull distributions of these statistics are obtained. It is shown that the powers of these statistics are coincident up to the order ?-1. For the case when ? is unknown, it is shown that TR(s) [greater, double equals] TL(s) [greater, double equals] TW(s) in their powers up to the order ?-1.

Asymptotic expansions for the standardized and Studentized estimates in the growth curve model

Abstract In this paper we obtain asymptotic expansions of the distribution functions of the standardized and Studentized estimates in the growth curve model and their error bounds. The results are obtained by using a general approximation theory (cf. Fujikoshi and Shimizu, Sugaku Expositions 3, 1990) of a scale mixture of the standard normal distribution. We also give a proof of a general result on a scale mixture of the standard normal distribution, based on a characteristic function method.