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Survey estimation of domain means that respect natural orderings

Many variables in surveys follow natural orderings that should be respected in estimates of domain means. For instance the U.S. 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 construct new design‐weighted constrained estimators. The resulting estimator is the classical design‐based domain estimator but after adaptive pooling of neighbouring domains, so that it is both readily implemented in large‐scale surveys and easy to explain to data users. Under mild conditions on the sampling design and the population we obtain the asymptotic properties of the estimator. Simulation results also demonstrate improved point estimators and confidence intervals for domain means using linearization‐ and replication‐based variance estimation compared to survey estimators that do not incorporate the constraints. The Canadian Journal of Statistics 44: 431–444; 2016 © 2016 Statistical Society of Canada