Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction
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Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction∗ YE Rendao · GE Wenting · LUO Kun
DOI: 10.1007/s11424-020-9216-7 Received: 23 July 2019 / Revised: 24 September 2019 c The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2020 Abstract In this paper, using the Bootstrap approach and generalized approach, the authors consider the one-sided hypothesis testing problems for variance component functions in the two-way random effects model. Firstly, the test statistics and confidence intervals for the sum of variance components are constructed. Next, the one-sided hypothesis testing problems for the ratio of variance components are also discussed. The Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases. Finally, the above approaches are applied to the real data examples of mice blood pH and molded plastic part’s dimensions. Keywords function.
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Bootstrap, generalized approach, two-way random effects model, variance component
Introduction
The two-way random effects model is widely used in quality control, experimental design, biomedical research, econometric modelling, market analysis and many other practical fields. For example, Wang, et al.[1] studied the impact of the plate material and ambient temperature of a specific type battery on its maximum output voltage using the two-way random effects model. Thompson[2] used this model to analyse the fuze burning time data with a view of estimating YE Rendao · GE Wenting School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China. Email: [email protected]. LUO Kun Alibaba Business College, Hangzhou Normal University, Hangzhou 310036, China. ∗ This research was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LY20A010019, Ministry of Education of China, Humanities and Social Science Projects under Grant No. 19YJA910006, Fundamental Research Funds for the Provincial Universities of Zhejiang under Grant No. GK199900299012-204, Zhejiang Provincial Philosophy and Social Science Planning Zhijiang Youth Project of China under Grant No. 16ZJQN017YB, Zhejiang Provincial Statistical Science Research Base Project of China under Grant No. 19TJJD08, and Scientific Research and Innovation Foundation of Hangzhou Dianzi University under Grant No. CXJJ2019008. This paper was recommended for publication by Editor TANG Niansheng.
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YE RENDAO · GE WENTING · LUO KUN
the precisions of the instruments. Cheng and Shao[3] considered five clinical trials and focused on the treatment-by-center interaction among them to discuss whether the treatment effect is significant or not. In view of the wide applications of variance component, research has been done about its parameter estimation problems. Some estimation methods has been established including analysis of variance, maximum likelihood, restricted maximum likelihood, spectral decomposition, and minimum norm quadratic unbiased estimation. See [4–10] for more details.
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