Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set (MACS) criterion. This criterion utilizes the area of the confidence set for the pivotal quantities, which are generated from the confidence set of the unknown parameters. Subsequently, we employ the MACS criterion to construct exact SCBs over any finite covariate intervals and to compare multiple SCBs of different forms. This approach can be used to determine the optimal SCBs. It is discovered that the area of the confidence set for the pivotal quantities of an asymmetric SCB is uniformly and can be very substantially smaller than that of the corresponding symmetric SCB. Therefore, under the MACS criterion, exact asymmetric SCBs should always be preferred. Furthermore, a new computationally efficient method is proposed to calculate the critical constants of exact SCBs for percentiles. A real data example on drug stability study is provided for illustration.

翻译：线性回归中百分位数的同时置信带（SCBs）是具有众多应用的重要工具。本文提出了一种用于比较百分位数SCBs的新准则——最小面积置信集（MACS）准则。该准则利用枢轴量的置信集面积，这些枢轴量源自未知参数置信集。随后，我们采用MACS准则在任意有限协变量区间上构建精确SCBs，并比较不同形式的多个SCBs。该方法可用于确定最优SCBs。研究发现，非对称SCB的枢轴量置信集面积一致地且显著地小于对应对称SCB的相应面积。因此，在MACS准则下，始终应优先选用精确非对称SCBs。此外，我们还提出了一种计算效率高的新方法，用于计算百分位数精确SCBs的临界常数值。通过药物稳定性研究的真实数据实例进行说明。