Bootstrap inference for unbalanced one-way classification model with skew-normal random effects

In this article, the one-sided hypothesis testing and interval estimation problems for fixed effect and variance component functions are considered in the unbalanced one-way classification model with skew-normal random effects. First, the Bootstrap approach is used to establish test statistics for fixed effects. Second, based on the matrix decomposition technique, Bootstrap approach and generalized approach, the test statistics, and confidence intervals for the single variance component and sum of variance components are constructed. Next, the exact test statistics for the ratio of variance components are obtained. The Monte Carlo simulation results indicate that the Bootstrap approach performs better than the generalized approach in most cases. Finally, the above approaches are illustrated with a real example of carbon fibers' strength.