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Tests for the second order stochastic dominance based on \(L\)-statistics. (English) Zbl 1214.62048

Summary: 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 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 \(L\)-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.

MSC:

62G10 Nonparametric hypothesis testing
60E15 Inequalities; stochastic orderings
62G30 Order statistics; empirical distribution functions
62P20 Applications of statistics to economics
65C05 Monte Carlo methods
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