🤖 AI Summary
This study addresses the challenge of constructing confidence intervals for the expectation of a target variable within the observed sample in small-area estimation. The authors propose a novel conditional conformal inference method that, under exchangeability or i.i.d. assumptions and within a regression framework, achieves finite-sample valid inference for the in-sample mean—a task previously unattainable with standard conformal prediction, which is inherently designed for out-of-sample prediction. By conditioning appropriately on the observed data, the proposed approach yields confidence intervals that rigorously maintain the prescribed coverage probability even when the underlying regression model is misspecified, thereby extending the applicability of conformal inference to internal estimation problems while preserving its nonparametric reliability guarantees.
📝 Abstract
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.