Nonparametric inference for second order stochastic dominance

Abstract

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. Thus, any results on stochastic dominance are in uenced by sampling errors. 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. We argue, however, that tests based on resampling techniques are more useful in practical applications. Their power in small samples is estimated by Monte Carlo simulations for a couple of alternative distributions. We further show that these tests can also be used for testing for first order stochastic dominance, often having a higher power than tests specifically designed for first order stochastic dominance such as the Kolmogorov-Smirnov test or the Wilcoxon-Mann-Whitney test. The results of this paper are relevant in various fields such as finance, life testing and decision under risk. --second order stochastic dominance,nonparametric inference,permutation tests,Monte Carlo methods