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

Abstract

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.

Keywords:

• Skew-normal population
• Moment estimation
• Maximum likelihood estimation
• Bootstrap approach
• Homogeneous test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F25
• 62F40

Acknowledgements

We gratefully acknowledge the editor and referees for their valuable comments and suggestions which greatly improve this paper.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research was supported by National Social Science Foundation of China (Grant No. 21BTJ068), Zhejiang Provincial Natural Science Foundation of China (Grant No.LY20A010019), and Ministry of Education of China, Humanities and Social Science Projects (Grant No.19YJA910006).