  This paper proposes a nonparametric test for $m$th-degree inverse stochastic
dominance which is a powerful tool for ranking distribution functions according
to social welfare. We construct the test based on empirical process theory. The
test is shown to be asymptotically size controlled and consistent. The good
finite sample properties of the test are illustrated via Monte Carlo
simulations. We apply our test to the inequality growth in the United Kingdom
from 1995 to 2010.
