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Survey estimation of domain means that respect natural orderings. (English. French summary) Zbl 1357.62056

Summary: 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.

MSC:

62D05 Sampling theory, sample surveys
62G08 Nonparametric regression and quantile regression
62P20 Applications of statistics to economics
62P05 Applications of statistics to actuarial sciences and financial mathematics
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