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Given samples from two non-negative random variables, we propose a family oftests for the null hypothesis that one random variable stochastically dominatesthe other at the second order. Test statistics are obtained as functionals ofthe difference between the identity and the Lorenz P-P plot, defined as thecomposition between the inverse unscaled Lorenz curve of one distribution andthe unscaled Lorenz curve of the other. We determine upper bounds for such teststatistics under the null hypothesis and derive their limit distribution, to beapproximated via bootstrap procedures. We then establish the asymptoticvalidity of the tests under relatively mild conditions and investigate finitesample properties through simulations. The results show that our testingapproach can be a valid alternative to classic methods based on the differenceof the integrals of the cumulative distribution functions, which requirebounded support and struggle to detect departures from the null in some cases.

A new class of nonparametric tests for second-order stochastic dominance based on the Lorenz P-P plot