Testing for Second-Order stochastic dominance of two distributions

Abstract

A distribution function F is said to stochastically dominate another distribution function G in the second-order sense if ∫^x_-∞F(u) du ≤ ∫^x_-∞G(u)du , for all x. Second-order stochastic dominance plays an important role in economics, finance, and accounting. Here a statistical test has been constructed to test H₀:∫^x_-∞F(u) du ≤ ∫^x_-∞G(u)du , for some x ∈ [a, b], against the hypothesis H₁:∫^x_-∞F(u) du > ∫^x_-∞G(u)du for all x ∈ [a, b], where a and b are any two real numbers. The test has been shown to be consistent and has an upper bound a on the asymptotic size. The test is expected to have usefulness for comparison of random prospects for risk averters.