共形置信区间及其在小区域估计中的应用
Conformal confidence intervals with an application to small area estimation
AI总结：
该研究提出一种新型共形推理方法，生成样本内结果未知期望的共形置信区间，填补经典回归与共形推理的空白，并将其应用于小区域估计问题。
AI中文摘要：
共形预测推理可针对可交换或独立同分布随机变量，生成具有指定覆盖概率的样本外随机结果区间。对于回归分析，即便回归函数存在不可避免的误设，在有限样本量下也能实现有效覆盖。我们提出一种新型共形推理方法，旨在针对已实现的样本，生成具有指定覆盖概率的样本内结果未知期望的置信区间。这些共形置信区间填补了经典回归与共形推理之间的空白，该方法被应用于小区域估计问题。
英文摘要：
Conformal prediction inference yields intervals for out-of-sample random outcomes with designated coverage probabilities, given exchangeable or independent-and-identically distributed random variables. For regression analysis, valid coverage can be achieved given finite sample sizes, despite unavoidable misspecifications of the regression function. We propose a novel method of conformal inference, aimed to produce confidence intervals of the unknown expectations of the in-sample outcomes with the designated coverage probabilities conditional on the realised sample. These conformal confidence intervals fill a gap between classical regression and conformal inference. The proposed approach is applied to small area estimation problems.
