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约束线性测量误差模型的统计推断

杨徐佳1,魏传华1,齐飞2   

  1. 1. 中央民族大学理学院, 北京 100081; 2.水利部发展研究中心投资与统计研究处,北京,100038
  • 收稿日期:2009-06-16 出版日期:2013-02-25 发布日期:2013-07-02

杨徐佳,魏传华,齐飞. 约束线性测量误差模型的统计推断[J]. 系统科学与数学, 2013, 33(2): 171-178.

YANG Xujia, WEI Chuanhua,QI Fei. STATISTICAL INFERENCE OF RESTRICTED LINEAR MEASUREMENT ERRORS REGRESSION MODELS[J]. Journal of Systems Science and Mathematical Sciences, 2013, 33(2): 171-178.

STATISTICAL INFERENCE OF RESTRICTED LINEAR MEASUREMENT ERRORS REGRESSION MODELS

YANG Xujia1, WEI Chuanhua1,QI Fei2   

  1. 1.School of Science, Minzu University of China, Beijing 100081; 2.Department of Investment and Statistics Research, Development Research Ministry of
    Water Resources of China, Beijing 100038
  • Received:2009-06-16 Online:2013-02-25 Published:2013-07-02
主要讨论线性测量误差模型在约束情况下的检验问题.基于比较原假设与备择假设下模型拟合残差平方和的思想构造了一种新的检验统计量, 该检验统计量在原假设下服从加权卡方分布.通过调整, 得到了一个渐近零分布为标准卡方分布的检验统计量. 最后,通过数值模拟验证了所提推断方法的有效性.
This paper considers testing for linear regression model when covariates are measured with additive error and some additional linear restrictions on the coefficients are available. We propose a test statistic based on the difference between the corrected residual sums of squares under the null and alterative hypotheses, and show that its limiting distribution is a weighted sum of independent chi-square distributions. We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Finally, some simulations are given to examine the performance of our procedure and the results are satisfactory.

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[1] 柏超. 两类线性模型回归系数的平衡LS估计及性质[J]. 系统科学与数学, 2013, 33(11): 1263-1271.
[2] 柏超. 一类线性模型中参数的平衡LS估计的性质[J]. 系统科学与数学, 2011, 31(7): 817-823.
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