We show that confidence intervals for a variance component or proportion, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results apply in settings where the variance or proportion is near or at the boundary of the parameter set. Simulations indicate the proposed test-statistics are approximately pivotal and lead to confidence intervals with near-nominal coverage even in small samples. We illustrate our methods' application in spatially-resolved transcriptomics where we compute approximately 15,000 confidence intervals, used for gene ranking, in less than 4 minutes. In the settings we consider, the proposed method is between two and 28,000 times faster than popular alternatives, depending on how many confidence intervals are computed.

翻译：我们证明，通过反转基于限制似然得分的某些检验统计量，可以获得方差分量或比例的一致渐近正确覆盖概率的置信区间。该结果适用于方差或比例接近或位于参数集边界的情况。模拟表明，所提出的检验统计量近似为枢轴量，即使在样本量较小的情况下也能生成接近名义覆盖率的置信区间。我们以空间分辨转录组学为例展示了该方法的应用：在不到4分钟内计算了约15，000个用于基因排序的置信区间。在本文考察的场景中，根据计算的置信区间数量，所提方法的速度是常用替代方法的2倍至28，000倍。