Testing for Second-Order Stochastic Dominance of Two Distributions

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