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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (6): 1144-1154.doi: 10.3969/j.issn.1005-3085.2024.06.011

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偏正态单向分类随机效应模型下暴露水平的Bootstrap推断

叶仁道,  杨嘉楠   

  1. 杭州电子科技大学经济学院，杭州 310018
  • 收稿日期:2022-03-03 接受日期:2022-08-21 出版日期:2024-12-15 发布日期:2024-12-15
  • 基金资助:
    国家社会科学基金 (21BTJ068)；全国统计科学研究重点项目 (2024LZ029).

Bootstrap Inference of Exposure Level with Skew-normal One-way Classification Random Effect Model

YE Rendao,  YANG Jianan   

  1. College of Economics, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2022-03-03 Accepted:2022-08-21 Online:2024-12-15 Published:2024-12-15
  • Supported by:
    The National Social Science Foundation of China (21BTJ068); the Key Project of National Statistical Science Research (2024LZ029).

摘要：

为评估工作环境中的暴露水平，基于偏正态单向分类随机效应模型，研究暴露水平的区间估计和假设检验问题。首先，利用EM算法给出未知参数的极大似然估计。进而，基于Bootstrap方法，构造个体平均暴露水平的三种Bootstrap置信区间。Monte Carlo模拟结果表明，修正的Bootstrap百分位置信区间在覆盖概率意义下优于其他两种Bootstrap置信区间，Bootstrap标准置信区间在置信上限意义下优于其他两种Bootstrap置信区间。最后，将上述方法应用于苯乙烯暴露数据的案例分析，以验证所提出方法的有效性和合理性。

关键词: 偏正态单向分类随机效应模型, 暴露水平, EM算法, Bootstrap置信区间

Abstract:

To assess exposure level in a work environment, we consider the interval estimation and hypothesis testing problems of exposure level based on the skew-normal one-way classification random effect model. Firstly, the EM algorithm is used to give the maximum likelihood estimation of unknown parameters. Secondly, based on the Bootstrap approach, three types of Bootstrap confidence intervals for the individual average exposure level are constructed. The Monte Carlo simulation results indicate that the improved percentile Bootstrap confidence interval performs best in the sense of coverage probability, and the Bootstrap standard confidence interval performs best in the sense of upper confidence limit. Finally, the above approaches are applied to the real data example of styrene exposures to verify the reasonableness and effectiveness of the proposed approaches.

Key words: skew-normal one-way classification random effect model, exposure level, EM algorithm, Bootstrap confidence interval

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