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.