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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 ›› 2015, Vol. 32 ›› Issue (2): 276-290.doi: 10.3969/j.issn.1005-3085.2015.02.012

• • 上一篇    下一篇

相协误差下线性模型回归系数的置信域(英)

李英华,   秦永松,   雷庆祝   

  1. 广西师范大学数学与统计学院，广西  桂林 541004
  • 收稿日期:2013-08-08 接受日期:2014-12-02 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家自然科学基金 (11271088; 11201088; 11361011)；广西自然科学基金项目 (2013GXNSFAA019004; 2013 gxnsfaa019007; 2013 gxnsfba019001).

Confidence Regions for Regression Coefficients in Linear Models under Associated Errors

LI Ying-hua,   QIN Yong-song,   LEI Qing-zhu   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004
  • Received:2013-08-08 Accepted:2014-12-02 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (11271088;  11201088;  11361011);  the Natural Science Foundation of Guangxi (2013GXNSFAA019004;  2013GXNSFAA019007;  2013GXNSFBA019001).

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摘要： 相协性在可靠性理论和统计领域中的一些重要模型中广泛出现．本文在平稳相协误差下研究了线性模型中回归系数的置信域的构造．在适当的条件下证明了回归系数的分组经验似然比统计量的渐近分布为卡方分布，并利用此结果构造了回归系数的经验似然置信域．

Abstract:

Association often occurs in certain reliability theory problems, as well as in some important models employed in statistical mechanics. In this paper, we investigate the construction of the confidence regions for the regression vector $\beta$ in a linear model under stationary and associated errors. It is shown that the blockwise empirical likelihood (EL) ratio statistic for $\beta$ asymptotically has $\chi^2$ distribution. The result is applied to obtain an EL-based confidence region for $\beta$.

Key words: linear models, blockwise empirical likelihood, associated sample, confidence region

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