A Test of Equality of Mean Vectors of Several Heteroscedastic Multivariate Populations

Abstract

This paper deals with a test of equality of mean vectors of several heteroscedastic multivariate populations. We derive not only the asymptotic expansion up to N −1 of the nonnull distribution of James's (1954) statistic, but also those of two corrected statistics due to Cordeiro and Ferrari (1991) and Kakizawa (1996). The derivation we considered here is based on the differential operator method developed in Kakizawa and Iwashita (2005).

Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions

“…. , 6) is identical to the coefficients which appeared in [36,37,34]). Here, the coefficients π k, 's, independent of ψ, are the sums of homogeneous polynomials of degrees 0, 1, 2, 3, 4 and 6 in Θ ε ; that is, π 1, = π [1] 1, + π [3] 1, ( = 0, 1, 2), π 1,3 = π [3] 1,3 , π 2, = π [0] 2, + π [2] 2, + π [4] 2, + π [6] 2, ( = 0, 1, 2, 3), π 2,4 = π [2] 2,4 + π [4] 2,4 + π [6] 2,4 , π 2,5 = π [4] 2,5 + π [6] 2,5 , π 2,6 = π [6] 2,6 (the explicit expressions, except for π [0] 2, , where the details can be obtained from author on request, are not reported here, to preserve space, since they are complicated and long formulae depending on K…”

“…The purpose of this paper is, as an extended study of Kakizawa and Iwashita [37], to obtain an asymptotic expansion for the nonnull distribution of T ψ up to order N −1 and then compare their local powers after either Bartlett's type adjustment or Cornish-Fisher's type size adjustment under nonnormality. Unlike Fujikoshi [26] and Wakaki et al [62], our derivation of asymptotic expansion is based on the differential operator method developed by Kakizawa and Iwashita [36,37] and Kakizawa [33][34][35].…”

A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions

“…We will evaluate (20) for t = 0 (the final results show that the formula remains valid even if t = 0). Recall that (4) implies˙ By the same argument as in Kakizawa and Iwashita [18] and Kakizawa [17], writing e(itF 0 ) = exp{itF 0 ( (1:q−1) +…”

“…The purpose of this paper is to obtain an asymptotic expansion for the nonnull distribution of T up to order N −1 without assuming the equality of the cumulants (1) j 1 ,...,j v = · · · = (q) j 1 ,...,j v (v 3), and then compare the third-order local powers of a class of one-way MANOVA tests. Unlike Kano [19] and Fujikoshi [12][13][14], our approach for obtaining an asymptotic expansion is based on the differential operator developed by Kakizawa and Iwashita [18] under nonnormality (see also [17]). Generalization to other problems on mean vectors, including GMANOVA model, will appear in a future work.…”

A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations

“…Under non-normality, Kakizawa and Iwashita (2008) obtained asymptotic expansions for the null distribution of Hotelling's T 2 -type counterpart of Welch's t-test statistic by including terms of order up to 1/n. Kakizawa (2007) obtained asymptotic expansions of James (1954) statistic for the one-way MANOVA layout. One major problem with James' statistic is that its application is rather too complicated when there are two or more factors.…”