Abstract
The hypothesis testing problems of unknown parameters for the variance components model with skew-normal random errors are discussed. Several properties of the model, such as the density function, moment generating function, and independence conditions, are obtained. A new version of Cochran’s theorem is given, which is used to establish exact tests for fixed effects and variance components of the model. For illustration, our main results are applied to two examples and a real data problem. Finally, some simulation results on the type I error probability and power of the proposed test are reported. And the simulation results indicate that the proposed test provides satisfactory performance on the type I error probability and power.
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Acknowledgments
This work is done during the visit of the first author to New Mexico State University. This material is based upon work funded by National Natural Science Foundation of China (Grant No. 11401148), National Social Science Foundation of China (Grant No. 12CJY012), Ministry of Education of China, Humanities and Social Science Projects (Grant No. 14YJC910005), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY14A010030), Zhejiang Provincial Philosophy and Social Science Planning Project of China (Grant No. 13NDJC089YB), and Houji Scholar Fund of Northwest A and F University, China. We gratefully acknowledge the editor and referees for their valuable comments and suggestions which greatly improve this paper.
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Ye, R., Wang, T., Sukparungsee, S. et al. Tests in variance components models under skew-normal settings. Metrika 78, 885–904 (2015). https://doi.org/10.1007/s00184-015-0532-1
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DOI: https://doi.org/10.1007/s00184-015-0532-1