Adaptive multigroup confidence intervals with constant coverage

Abstract

Commonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average, but their actual coverage rate for a given group will be above or below the nominal rate, depending on the group mean. While correct coverage for a given group can be achieved with a standard t -interval, this approach is not adaptive to the available information about the distribution of group-specific means. In this article we construct confidence intervals that have a constant frequentist coverage rate and that make use of information about across-group heterogeneity, resulting in constant-coverage intervals that are narrower than standard t -intervals on average across groups. Such intervals are constructed by inverting biased Bayes-optimal tests for the mean of each group, where the prior distribution for a given group is estimated with data from the other groups.