NONPARAMETRIC TESTS OF DENSITY RATIO ORDERING
Brendan Beare () and
Econometric Theory, 2015, vol. 31, issue 3, 471-492
We study a family of nonparametric tests of density ratio ordering between two continuous probability distributions on the real line. Density ratio ordering is satisfied when the two distributions admit a nonincreasing density ratio. Equivalently, density ratio ordering is satisfied when the ordinal dominance curve associated with the two distributions is concave. To test this property, we consider statistics based on the L p -distance between an empirical ordinal dominance curve and its least concave majorant. We derive the limit distribution of these statistics when density ratio ordering is satisfied. Further, we establish that, when 1 â‰¤ p â‰¤ 2, the limit distribution is stochastically largest when the two distributions are equal. When 2
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