Optimal Conformal Prediction for Small Areas

Abstract

Abstract Existing methods for small-area data involve a trade-off between maintaining area-level frequentist coverage rates and improving precision via the incorporation of indirect information. In this article, we develop an area-level prediction region procedure that mitigates this trade-off. The method takes a conformal prediction approach in which the conformity measure is the posterior predictive density of a working model that incorporates indirect information. The resulting prediction region has guaranteed within-area frequentist coverage regardless of the working model, and, if the working model assumptions are accurate, the region has smaller expected volume compared to other regions with the same coverage rate. For a normal working model, we prove such a prediction region is an interval and construct a straightforward algorithm to obtain its endpoints. We illustrate the performance of our method through simulation studies and an application to EPA radon survey data.