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S. Johansen, “The Welch-James Approximation to the Distribution of the Residual Sum of Squares in a Weighted linear Regression,” Biometrika, Vol. 67, No. 1, 1980, pp. 85-95. doi:10.1093/biomet/67.1.85

has been cited by the following article:

• TITLE: An Approximate Hotelling T2-Test for Heteroscedastic One-Way MANOVA

  AUTHORS: Jin-Ting Zhang

  KEYWORDS: Approximate Hotelling T2Test; Multivariate k-Sample Behrens-Fisher Problem; Wishart-Approximation; Wishart Mixture

  JOURNAL NAME: Open Journal of Statistics, Vol.2 No.1, January 19, 2012

  ABSTRACT: In this paper, we consider the general linear hypothesis testing (GLHT) problem in heteroscedastic one-way MANOVA. The well-known Wald-type test statistic is used. Its null distribution is approximated by a Hotelling T2 distribution with one parameter estimated from the data, resulting in the so-called approximate Hotelling T2 (AHT) test. The AHT test is shown to be invariant under affine transformation, different choices of the contrast matrix specifying the same hypothesis, and different labeling schemes of the mean vectors. The AHT test can be simply conducted using the usual F-distribution. Simulation studies and real data applications show that the AHT test substantially outperforms the test of [1] and is comparable to the parametric bootstrap (PB) test of [2] for the multivariate k-sample Behrens-Fisher problem which is a special case of the GLHT problem in heteroscedastic one-way MANOVA.