Semi-nonparametric test of second degree stochastic dominance with respect to a function

In an expected utility framework, assuming a decision maker operates under utility k([dot operator][theta]), for two risky alternatives X and Y with respective distribution functions F and G, alternative X is said to dominate alternative Y with respect to k([dot operator][theta]) if for all y. Utilizing the empirical distribution functions of F and G, a statistical test is presented to test the null hypothesis of indifference between X and Y given k([dot operator][theta]) against the hypothesis that X dominates Y with respect to k([dot operator][theta]). This is a large sample testing application of stochastic dominance with respect to a function. The asymptotic distribution of the test statistic associated with the null hypothesis given a sub-set of the utility function parameter space is developed. Based on large sample rejection regions, the hypothesis of preference of one alternative over another is demonstrated with an empirical example.