  This paper makes the following original contributions. First, we develop a
unifying framework for testing shape restrictions based on the Wald principle.
The test has asymptotic uniform size control and is uniformly consistent.
Second, we examine the applicability and usefulness of some prominent shape
enforcing operators in implementing our framework. In particular, in stark
contrast to its use in point and interval estimation, the rearrangement
operator is inapplicable due to a lack of convexity. The greatest convex
minorization and the least concave majorization are shown to enjoy the analytic
properties required to employ our framework. Third, we show that, despite that
the projection operator may not be well-defined/behaved in general parameter
spaces such as those defined by uniform norms, one may nonetheless employ a
powerful distance-based test by applying our framework. Monte Carlo simulations
confirm that our test works well. We further showcase the empirical relevance
by investigating the relationship between weekly working hours and the annual
wage growth in the high-end labor market.
