TESTING FOR 2ND-ORDER STOCHASTIC-DOMINANCE OF 2 DISTRIBUTIONS

A distribution function F is said to stochastically dominate another distribution function G in the second-order sense if integral-x/-infinity F(u) du less-than-or-equal-to integral-x/-infinity 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: integral-x/-infinity F(u) du less-than-or-equal-to integral-x/-infinity G(u) du, for some x is-an-element-of [a, b], against the hypothesis H1:integral-x/-infinity F(u) du > integral-x/-infinity G(u) du, for all x is-an-element-of [a, b], where a and b are any two real numbers. The test has been shown to be consistent and has an upper bound alpha on the asymptotic size. The test is expected to have usefulness for comparison of random prospects for risk averters.