  In the analysis of survey data it is of interest to estimate and quantify
uncertainty about means or totals for each of several non-overlapping
subpopulations, or areas. When the sample size for a given area is small,
standard confidence intervals based on data only from that area can be
unacceptably wide. In order to reduce interval width, practitioners often
utilize multilevel models in order to borrow information across areas,
resulting in intervals centered around shrinkage estimators. However, such
intervals only have the nominal coverage rate on average across areas under the
assumed model for across-area heterogeneity. The coverage rate for a given area
depends on the actual value of the area mean, and can be nearly zero for areas
with means that are far from the across-group average. As such, the use of
uncertainty intervals centered around shrinkage estimators are inappropriate
when area-specific coverage rates are desired. In this article, we propose an
alternative confidence interval procedure for area means and totals under
normally distributed sampling errors. This procedure not only has constant
$1-\alpha$ frequentist coverage for all values of the target quantity, but also
uses auxiliary information to borrow information across areas. Because of this,
the corresponding intervals have shorter expected lengths than standard
confidence intervals centered on the unbiased direct estimator. Importantly,
the coverage of the procedure does not depend on the assumed model for
across-area heterogeneity. Rather, improvements to the model for across-area
heterogeneity result in reduced expected interval width.
