A note on fiducial generalized pivots for in one-way heteroscedastic ANOVA with random effects

Abstract

The paper deals with generalized confidence intervals for the between-group variance in one-way heteroscedastic (unbalanced) ANOVA with random effects. The approach used mimics the standard one applied in mixed linear models with two variance components, where interval estimators are based on a minimal sufficient statistic derived after an initial reduction by the principle of invariance. A minimal sufficient statistic under heteroscedasticity is found to resemble its homoscedastic counterpart and further analogies between heteroscedastic and homoscedastic cases lead us to two classes of fiducial generalized pivots for the between-group variance. The procedures suggested formerly by Wimmer and Witkovský [Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model, J. Stat. Comput. Simul. 73 (2003), pp. 333–346] and Li [Comparison of confidence intervals on between group variance in unbalanced heteroscedastic one-way random models, Comm. Statist. Simulation Comput. 36 (2007), pp. 381–390] are found to belong to these two classes. We comment briefly on some of their properties that were not mentioned in the original papers. In addition, properties of another particular generalized pivot are considered.

Keywords:

• unbalanced ANOVA
• heteroscedasticity
• fiducial generalized pivots
• random effects
• between-group variance

AMS Classification :

• 62F25
• 62J10

Acknowledgements

This work was supported by the Slovak Research and Development Agency under the contract No. LPP-0388-09. In part, it was also supported by the grant VEGA 1/0077/09.