论文标题
利用不确定的先前信息的通用回归模型中的置信区间
Confidence intervals in general regression models that utilize uncertain prior information
论文作者
论文摘要
我们考虑一个通用回归模型，没有比例参数。我们的目的是为$θ$的标量参数构建一个置信区间，该参数利用了不确定的先前信息，即独特的标量参数$τ$采用指定的值$ t $。此置信区间应具有良好的覆盖范围。它也应该具有缩放的预期长度，而相对于通常的置信区间的缩放时间，当先前信息正确时，（a）的最大值不太大，而当数据和先验信息高度不和谐时，（c）的最大值接近1。在线性回归的特定情况下，最大似然估计器$θ$和$τ$的渐近关节分布与这些估计量的联合分布相似，其正态分布错误具有已知方差。这种相似性用于使用使用R软件包Ciuupi计算的置信区间来构建具有所需属性的置信区间，该置信区间在此特定的线性回归案例中利用了不确定的先验信息。此置信区间的一个重要实际应用是对进行数量的生物测定法进行比较两种类似的化合物。在这种情况下，不确定的先前信息是“并行性”的假设存在。我们提供了广泛的数值结果，以说明在这种情况下此置信区间的特性。
We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $θ$ that utilizes the uncertain prior information that a distinct scalar parameter $τ$ takes the specified value $t$. This confidence interval should have good coverage properties. It should also have scaled expected length, where the scaling is with respect to the usual confidence interval, that (a) is substantially less than 1 when the prior information is correct, (b) has a maximum value that is not too large and (c) is close to 1 when the data and prior information are highly discordant. The asymptotic joint distribution of the maximum likelihood estimators $θ$ and $τ$ is similar to the joint distributions of these estimators in the particular case of a linear regression with normally distributed errors having known variance. This similarity is used to construct a confidence interval with the desired properties by using the confidence interval, computed using the R package ciuupi, that utilizes the uncertain prior information in this particular linear regression case. An important practical application of this confidence interval is to a quantal bioassay carried out to compare two similar compounds. In this context, the uncertain prior information is that the hypothesis of "parallelism" holds. We provide extensive numerical results that illustrate the properties of this confidence interval in this context.
