Bootstrap tests of stochastic dominance with asymptotic similarity on the boundary

We propose a new method of testing stochastic dominance which improves on existing tests based on bootstrap or subsampling. 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 in…nite as well as …nite dimensional unknown parameters, so that the variables may be residuals from nonparametric and semiparametric models. Our simulation results show that our tests are indeed more powerful than the existing subsampling and recentered bootstrap. Key words and Phrases: Set estimation; Size of test; Unbiasedness; Similarity; Bootstrap; Subsampling. JEL Classi…cations: C12, C14, C52. 1Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom. E-mail address: [email protected]. Thanks to the ESRC and Leverhulme foundations for …nancial support. 2Department of Economics, University of Pennsylvania, 528 McNeil Building, 3718 Locust Walk, Philadelphia, Pennsylvania 19104-6297. Email: [email protected] 3Department of Economics, Seoul National University, Seoul 151-742, Korea. E-mail address: [email protected]. Thanks to the Korea Research Foundation for …nancial support.