Comparison of confidence intervals for the Behrens-Fisher problem

The Behrens-Fisher problem concerns the inferences for the difference between means of two independent normal populations without the assumption of equality of variances. In this article, we compare three approximate confidence intervals and a generalized confidence interval for the Behrens-Fisher problem. We also show how to obtain simultaneous confidence intervals for the three population case (analysis of variance, ANOVA) by the Bonferroni correction factor. We conduct an extensive simulation study to evaluate these methods in respect to their type I error rate, power, expected confidence interval width, and coverage probability. Finally, the considered methods are applied to two real dataset.