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Journal of Probability and Statistics
Volume 2011, Article ID 484272, 10 pages
Research Article

Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

1Department of Statistics, University of Central Florida, Orlando, FL 32816, USA
2School of Nursing, University of Alabama at Birmingham, Birmingham, AL 35294, USA

Received 22 May 2011; Accepted 8 August 2011

Academic Editor: Alan M. Polansky

Copyright © 2011 Xin Yan and Xiaogang Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method.