Approximate interval for the between-group variance under heteroscedasticity

Abstract

The paper presents an approximate confidence interval for the between-group variance in a one-way heteroscedastic random-effects model. Derivation of the interval is inspired by the ideas in Williams [A confidence intervals for variance components, Biometrika 49 (1962), pp. 278–281] for the homoscedastic case. Simulations suggest that the proposed interval performs better than or comparably to the other available procedures as studied in 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], Hartung and Knapp [On confidence intervals for the among-group variance in the one-way random effects model with unequal error variances, J. Statist. Plann. Inference 127 (2005), pp. 157–177], 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]. Moreover, it is relatively easy to compute.

Keywords:

• variance components
• heteroscedasticity
• one-way ANOVA
• approximate confidence intervals

2010 AMS Subject Classifications :

• 62J10
• 62F25

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 grants VEGA 1/0077/09 and VEGA 2/0019/10.