Search

This article addresses derivation and existence of quadratic forms that were suggested by Burch (2007) for procedures for inference on variance components in mixed linear models in combination with generalized fiducial inference. A relatively simple algorithm leading to the required quadratic forms in a general 3-variance-component model is stated and designs for two-way ANOVA models without interactions that permit Burch's procedure are characterized. This complements developments in the original article by Burch.

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 rel...

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. Sim...

The paper deals with construction of confidence intervals for the variance component in the family of distributions using generalized p-values. Unfortunately, when W has more than two different eigen values, the nonuniqueness of the appropriate test variable occurs. This was illustrated by Zhou and Mathew [Zhou, L. and Mathew, T., 1994, Some tests for variance components using generalized p-values. Technometrics, 36, 394–402.] on an example of a generalized test variable dependent on positive constants c i and as Zhou and Mathew mentioned, it is not clear which test variable is preferred in this situation. In the paper, we make a choice of c i inspired by some known test statistics used for testing the nullity of . Also another test variable, which cannot be derived from Zhou’s and Mathew’s, is stated and all mentioned test variables are compared.