Simultaneous confidence intervals for comparing several inverse Gaussian means under heteroscedasticity

ABSTRACT

Recently, Zhang [Simultaneous confidence intervals for several inverse Gaussian populations. Stat Probab Lett. 2014;92:125–131] proposed simultaneous pairwise confidence intervals (SPCIs) based on the fiducial generalized pivotal quantity concept to make inferences about the inverse Gaussian means under heteroscedasticity. In this paper, we propose three new methods for constructing SPCIs to make inferences on the means of several inverse Gaussian distributions when scale parameters and sample sizes are unequal. One of the methods results in a set of classic SPCIs (in the sense that it is not simulation-based inference) and the two others are based on a parametric bootstrap approach. The advantages of our proposed methods over Zhang’s (2014) method are: (i) the simulation results show that the coverage probability of the proposed parametric bootstrap approaches is fairly close to the nominal confidence coefficient while the coverage probability of Zhang’s method is smaller than the nominal confidence coefficient when the number of groups and the variance of groups are large and (ii) the proposed set of classic SPCIs is conservative in contrast to Zhang’s method.

KEYWORDS:

• Conservative
• coverage probability
• fiducial generalized pivotal
• heteroscedasticity
• simulation

Acknowledgements

We would like to acknowledge the referee for his/her constructive comments. The authors would like to acknowledge the Research Council of Shiraz University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors advise no direct funding is associated with the research reported in this article.