Some Aspects of Multivariate Behrens-Fisher Problem

In this paper we discuss the well known multivariate Behrens-Fisher problem which deals with testing the equality of two normal mean vectors under heteroscedasticity of dispersion matrices. Some existing tests are reviewed and a new test based on Roy's union-intersection principle coupled with the generalized P-value is proposed. The tests are compared with respect to size and power based on simulation, and applied to a few useful data sets. AMS (2000) Subject Classification : 62H10, 62H15.

[1]  A. C. Rencher.  Methods of multivariate analysis , 1995 .

[2]  Seong-Ju Kim.  A practical solution to the multivariate Behrens-Fisher problem , 1992 .

[3]  Ying Yao,et al.  An approximate degrees of freedom solution to the multivariate Behrens-Fisher problem* , 1965 .

[4]  D. G. Nel,et al.  A solution to the multivariate behrens-fisher problem , 1986 .

[5]  Generalized p-values and the multivariate Behrens-Fisher problem , 1997 .

[6]  William F. Christensen,et al.  A comparison of type i error rates and power levels for seven solutions to the multivariate behrens-fisher problem , 1997 .

[7]  Zheng Qing-shan.  Statistical methods of Meta-analysis , 2005 .

[8]  Sam Weerahandi,et al.  Size performance of some tests in one-way anova , 1998 .

[9]  Kam-Wah Tsui,et al.  Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters , 1989 .

[10]  George E. P. Box,et al.  Some Aspects of Multivariate Analysis , 2011 .

[11]  K. Krishnamoorthy,et al.  Modified Nel and Van der Merwe test for the multivariate Behrens–Fisher problem , 2004 .

[12]  Donald R. Jensen,et al.  Fundamentals of Multivariate Analysis Part II. Inference About Two Treatments , 1969 .

[13]  Thomas Mathew,et al.  Generalized p -values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA , 2004 .

[14]  Xiao-Hua Zhou,et al.  Statistical Methods for Meta‐Analysis , 2008 .

[15]  Ramon C. Littell,et al.  Exact Statistical Methods for Data Analysis , 2001, Technometrics.

[16]  Alvin C. Rencher,et al.  Methods of multivariate analysis (second edition) , 2002 .

[17]  Samaradasa Weerahandi,et al.  Generalized Confidence Intervals , 1993 .

[18]  S. Kullback,et al.  Some Aspects of Multivariate Analysis. , 1958 .

[19]  S. Johansen,et al.  The Welch - James approximation to the distribution of the residual sum of squares in a weighted lin , 1980 .

[20]  Sam Weerahandi,et al.  Exact Statistical Methods for Data Analysis , 1998, Journal of the American Statistical Association.

[21]  Søren Johansen,et al.  Amendments and Corrections: The Welch--James Approximation to the Distribution of the Residual Sum of Squares in a Weighted Linear Regression , 1982 .