Consistent Testing for Stochastic Dominance under General Sampling Schemes∗

We propose a procedure for estimating the critical values of the extended KolmogorovSmirnov tests of Stochastic Dominance of arbitrary order in the general K-prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some N−1/2 local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We describe an alternative method for obtaining critical values based on recentering the test statistic and using full sample bootstrap methods. We compare the two methods in theory and in practice. ∗We would like to thank three referees, Joel Horowitz, Hashem Pesaran, Bernard Salanié, Steve Satchell, and Michael Wolf for helpful comments. †Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom. E-mail address: [email protected]. My research was supported by the Economic and Social Research Council of the United Kingdom and the Cowles Foundation. ‡Department of Economics, Southern Methodist University, Dallas, Texas, 75275-0496. Email: [email protected]. §Department of Economics, Korea University, Seoul 136-701, Korea. Email Address : [email protected] I would like to thank the hospitality of the Cowles Foundation during my visits. This work was supported by the Korea Research Foundation.