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Bootstrap Tests of Stochastic Dominance with AsymptoticSimilarity on the Boundary

By Oliver Linton, Kyungchul Song and Yoon-Jae Whang

Abstract

We propose a new method of testing stochastic dominance which improves onexisting tests based on bootstrap or subsampling. Our test requires estimation ofthe contact sets between the marginal distributions. Our tests have asymptoticsizes that are exactly equal to the nominal level uniformly over the boundarypoints of the null hypothesis and are therefore valid over the whole null hy-pothesis. We also allow the prospects to be indexed by in…nite as well as …nitedimensional unknown parameters, so that the variables may be residuals fromnonparametric and semiparametric models. Our simulation results show thatour tests are indeed more powerful than the existing subsampling and recenteredbootstrap.Set estimation, Size of test, Unbiasedness, Similarity,Bootstrap, Subsampling.

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