Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null hypothesis of zero first-order autocorrelation of the random errors against the alternative hypothesis of positive first-order autocorrelation. If this null hypothesis is accepted then the confidence interval centred on the Ordinary Least Squares estimator is used; otherwise the confidence interval centred on the Feasible Generalized Least Squares estimator is used. We provide new tools for the computation, for any given design matrix and parameter of interest, of graphs of the coverage probability functions of the confidence interval resulting from this two-stage procedure and the confidence interval that is always centred on the Feasible Generalized Least Squares estimator. These graphs are used to choose the better confidence interval, prior to any examination of the observed response vector.

中文翻译：

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Durbin-Watson 预检验对回归置信区间的影响

考虑一个线性回归模型，并假设我们的目标是为回归参数的指定线性组合找到置信区间。在实践中，通常对随机误差的零一阶自相关的零假设与正一阶自相关的替代假设进行 Durbin-Watson 预检验。如果接受该原假设，则使用以普通最小二乘估计量为中心的置信区间；否则使用以可行广义最小二乘估计量为中心的置信区间。我们为任何给定的设计矩阵和感兴趣的参数提供新的计算工具，由这个两阶段过程产生的置信区间的覆盖概率函数图和始终以可行广义最小二乘估计量为中心的置信区间。在对观察到的响应向量进行任何检查之前，这些图用于选择更好的置信区间。