Simultaneous confidence intervals for one-way layout based on generalized pivotal quantities

Abstract

In this paper, we consider simultaneous confidence intervals for all-pairwise comparisons of treatment means in a one-way layout under heteroscedasticity. Two kinds of simultaneous intervals are provided based on the fiducial generalized pivotal quantities of the interest parameters. We prove that they both have asymptotically correct coverage. Simulation results and an example are also reported. It is concluded from calculational evidence that the second kind of simultaneous confidence intervals, which we provide, performs better than existing methods.

Keywords:

• one-way layout
• frequentist property
• generalized pivotal quantity
• heteroscedasticity
• simultaneous confidence interval

2000 AMS Subject Classfications :

• 62J10
• 62J15

Acknowledgements

Xiong's research was supported partly by the National Natural Science Foundation of China (Grant No. 10771126), and Mu's research was supported partly by the National Natural Science Foundation of China (Grant No. 10771015). We thank the Associate Editor and the Reviewer very much for their constructive comments and suggestions.