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：百分位数联合置信带（SCB）是线性回归中具有广泛应用价值的工具。本文提出了一种用于比较百分位数SCB的新准则，称为最小区域置信集（MACS）准则。该准则利用由未知参数置信集生成的关键量置信集的面积，进而采用MACS准则在任意有限协变量区间上构建精确SCB，并比较不同形式的多个SCB。这一方法可用于确定最优SCB。研究发现，非对称SCB关键量置信集的面积一致性地且大幅小于相应对称SCB的面积。因此，在MACS准则下，应始终优先选择精确的非对称SCB。此外，本文提出了一种新的高效计算方法，用于计算百分位数精确SCB的临界常数。最后，通过一个关于药品稳定性研究的真实数据示例进行说明。