Nonparametric Inference for Second Order Stochastic Dominance

This paper deals with nonparametric inference for second order stochastic dominance of two random variables. If their distribution functions are unknown they have to be inferred from observed realizations. We establish two methods to take the sampling error into account. The first one is based on the asymptotic normality of point estimators, while the second one, relying on resampling techniques, can also cope with small sample sizes. Both methods are used to develop statistical tests for second order stochastic dominance. However, tests based on resampling techniques are more useful in practical applications. Their small sample power is estimated by Monte Carlo simulations for various alternative distributions.