We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce the problem of exact selective inference to a bivariate truncated Gaussian distribution. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi and Taylor (2022). Yet our pivot always produces narrower confidence intervals than a closely related data splitting procedure. We investigate the trade-off between power and exact selective inference on simulated datasets and an HIV drug resistance dataset.

翻译：摘要：我们提出了一种用于带随机化的精确选择性推断的枢轴量。该枢轴量不仅能在高斯回归模型中实现精确推断，还可以表示为闭合形式。我们将精确选择性推断问题简化为二元截断高斯分布。尽管这样做牺牲了Panigrahi与Taylor（2022）中基于近似极大似然估计所获得的统计功效，但我们的枢轴量始终能比紧密相关的数据分裂方法产生更窄的置信区间。我们通过模拟数据集和HIV耐药性数据集，研究了统计功效与精确选择性推断之间的权衡关系。