Extensions are presented to the results of Davidson and Duclos (2007), whereby the null
hypothesis of restricted stochastic non dominance can be tested by both asymptotic and
bootstrap tests, the latter having considerably better properties as regards both size and
power. In this paper, the methodology is extended to tests of higher-order stochastic dominance.
It is seen that, unlike the first-order case, a numerical nonlinear optimisation problem
has to be solved in order to construct the bootstrap DGP. Conditions are provided for a
solution to exist for this problem, and efficient numerical algorithms are laid out. The empirically
important case in which the samples to be compared are correlated is also treated,
both for first-order and for higher-order dominance. For all of these extensions, the bootstrap
algorithm is presented. Simulation experiments show that the bootstrap tests perform
considerably better than asymptotic tests, and yield reliable inference in moderately sized
samples.
Almost Higher Order Stochastic Dominance
