We show that confidence intervals in a variance component model, 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 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特定检验统计量，可以在方差分量模型中构建具有渐近正确均匀覆盖概率的置信区间。该方法适用于方差接近或处于参数集边界的情况。模拟结果表明，所提出的检验统计量近似枢轴量，即使在较小样本量下也能产生接近名义覆盖水平的置信区间。我们以空间分辨转录组学为例展示方法应用，在4分钟内计算了约15,000个用于基因排序的置信区间。在考察场景中，本方法比常用替代方案快2至28,000倍，具体加速倍数取决于需计算的置信区间数量。