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In this paper, we consider the one-sided hypothesis testing problems for variance component functions in the unbalanced two-way random effects model. Firstly, using the Bootstrap approach and generalized approach, the test statistics and confidence intervals for the sum and ratio of variance components are constructed respectively. Next, 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 example of the efficiency of assembly lines workers in a manufacturing plant.

Bootstrap inference on variance component functions in the unbalanced two-way random effects model