A parametric bootstrap approach for one-way classification model with skew-normal random effects

In this paper, several properties of one-way classification model with skew-normal random effects are obtained, such as moment generating function, density function and noncentral skew chi-square distribution, etc. Based on the EM algorithm, we discuss the maximum likelihood (ML) estimation of unknown parameters. For testing problem of fixed effect, a parametric bootstrap (PB) approach is developed. Finally, some simulation results on the Type I error rates and powers of the PB approach are obtained, which show that the PB approach provides satisfactory performances on the Type I error rates and powers, even for small samples. For illustration, our main results are applied to a real data problem.