Survey estimators that respect natural orderings

Many variables in surveys follow natural orderings that should be respected in estimates of domain means. For instance, the National Compensation Survey estimates mean wages for many job categories, and these mean wages are expected to be non-decreasing according to job level. In this type of situation, isotonic regression can be applied to give constrained estimators satisfying the monotonicity. We combine domain estimation and the pooled adjacent violators algorithm to 10 construct new design-weighted constrained estimators. Under mild conditions on the sampling design and the population, the estimators are shown to be design consistent and asymptotically normal. Confidence intervals for domain means using linearization-based and replication-based variance estimation show marked improvements compared to survey estimators that do not incorporate the constraints. 15