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In this paper, the one-sided hypothesis testing and interval estimation problems for the fixed effect and variance component functions are considered in the skew-normal unbalanced heteroscedastic one-way classification random effects model. Firstly, the Bootstrap approach is used to establish test statistic for fixed effect. Secondly, the test statistics and confidence intervals for variance component functions are constructed by Bootstrap approach and generalized approach, and their theoretical properties are discussed. 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 two real examples of the annual average concentrations of fine particulate matter and nitrogen dioxide.

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