Tests for the Second Order Stochastic Dominance Based on <italic>L</italic>-Statistics

We use some characterizations of convex and concave-type orders to define discrepancy measures useful in two testing problems involving stochastic dominance assumptions. The results are connected with the mean value of the order statistics and have a clear economic interpretation in terms of the expected cumulative resources of the poorest (or richest) in random samples. Our approach mainly consists of comparing the estimated means in ordered samples of the involved populations. The test statistics we derive are functions of <italic>L</italic>-statistics and are generated through estimators of the mean order statistics. We illustrate some properties of the procedures with simulation studies and an empirical example.