Bootstrap inference of the skew-normal two-way classification random effects model with interaction

In this paper, we consider the statistical inference problems for the fixed effect and variance component functions in the two-way classification random effects model with skew-normal errors. Firstly, the exact test statistic for the fixed effect is constructed. Secondly, using the Bootstrap approach and generalized approach, the one-sided hypothesis testing and interval estimation problems for the single variance component, the sum and ratio of variance components are discussed respectively. Further, the Monte Carlo simulation results indicate that the exact test statistic performs well in the one-sided hypothesis testing problem for the fixed effect. And the Bootstrap approach is better than the generalized approach in the one-sided hypothesis testing problems for variance component functions in most cases. Finally, the above approaches are applied to the real data examples of the consumer price index and value-added index of three industries to verify their rationality and effectiveness.