Bootstrap Tests of Stochastic Dominance with Asymptotic Similarity on the Boundary

Abstract

We propose a new method of testing stochastic dominance which improves on existing tests based on bootstrap or sub-sampling. Our test requires estimation of the contact sets between the marginal distributions. Our tests have asymptotic sizes that are exactly equal to the nominal level uniformly over the boundary points of the null hypothesis and are therefore valid over the whole null hypothesis. We also allow the prospects to be indexed by infinite as well as finite dimensional unknown parameters, so that the variables may be residuals from nonparametric and semi-parametric models. Our simulation results show that our tests are indeed more powerful than the existing sub-sampling and recentered bootstrap.

Keywords: Set estimation, Size of test, Unbiasedness, Similarity, Bootstrap, Subsampling

JEL Classification: C12, C14, C52