Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction

Abstract

In this paper, using the Bootstrap approach and generalized approach, the authors consider the one-sided hypothesis testing problems for variance component functions in the two-way random effects model. Firstly, the test statistics and confidence intervals for the sum of variance components are constructed. Next, the one-sided hypothesis testing problems for the ratio of variance components are also discussed. The Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases. Finally, the above approaches are applied to the real data examples of mice blood pH and molded plastic part’s dimensions.