COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1713 An Improved Bootstrap Test of Stochastic Dominance Oliver Linton (London School of Economics), Kyungchul Song (University
of Pennsylvania) July 2009 We propose a new method of testing stochastic dominance that improves on existing tests
based on the standard bootstrap or subsampling. The method admits prospects involving
infinite as well as finite dimensional unknown parameters, so that the variables are
allowed to be residuals from nonparametric and semiparametric models. The proposed
bootstrap tests have asymptotic sizes that are less than or equal to the nominal level
uniformly over probabilities in the null hypothesis under regularity conditions. This
paper also characterizes the set of probabilities that the asymptotic size is exactly
equal to the nominal level uniformly. As our simulation results show, these
characteristics of our tests lead to an improved power property in general. The
improvement stems from the design of the bootstrap test whose limiting behavior mimics the
discontinuity of the original test's limiting distribution. |
