Approximate interval for the between-group variance under heteroscedasticity
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 Witkovsky [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.
heteroscedasticity approximate confidence intervals variance components one-way anova