  Population domain means are frequently expected to respect shape or order
constraints that arise naturally with survey data. For example, given a job
category, mean salaries in big cities might be expected to be higher than those
in small cities, but no order might be available to be imposed within big or
small cities. A design-based estimator of domain means that imposes constraints
on the most common survey estimators is proposed. Inequality restrictions that
can be expressed with irreducible matrices are considered, as these cover a
broad class of shapes and partial orderings. The constrained estimator is shown
to be consistent and asymptotically normally distributed under mild conditions,
given that the shape is a reasonable assumption for the population. Further,
simulation experiments demonstrate that both estimation and variability of
domain means are improved by the constrained estimator in comparison with usual
unconstrained estimators, especially for small domains. An application of the
proposed estimator to the 2015 U.S. National Survey of College Graduates is
shown.
