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When the scale parameters and skewness parameters are unknown, we consider the problem of homogeneous test of location parameters in several skew-normal populations. First, the conditional test statistic is constructed and its approximate distribution is proved. Second, we estimate the unknown parameters based on the methods of moment and maximum likelihood estimation. Then we construct the Bootstrap test statistics and generalize the results of Xu from normal population to skew-normal population. Further, the Monte-Carlo simulation results indicate that in terms of controlling the Type I error probability, the Bootstrap test statistic based on the moment estimator performs better than that based on the maximum likelihood estimator. Finally, the above approaches are illustrated with two real examples of gross domestic product and turbine bearing performance.

Bootstrap approaches for homogeneous test of location parameters under skew-normal settings