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Testing the concavity of an ordinaldominance curve

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  • Beare, Brendan K.
  • Moon, Jong-Myun

Abstract

We study the asymptotic properties of a class of statistics used for testing the null hypothesis that an ordinal dominance curve is concave. The statistics are based on the Lp-distance between the empirical ordinal dominance curve and its least concave majo- rant, with 1 ≤ p ≤ ∞. We formally establish the limit distribution of the statistics when the true ordinal dominance curve is concave. Further, we establish that, when 1 ≤ p ≤ 2, the limit distribution is stochastically largest when the true ordinal dominance curve is the 45-degree line. When p > 2, this is not the case, and in fact the limit distribution diverges to infinity along a suitably chosen sequence of concave ordinal dominance curves. Our results serve to clarify, extend and amend assertions appearing previously in the literature for the cases p = 1 and p = ∞.

Suggested Citation

  • Beare, Brendan K. & Moon, Jong-Myun, 2012. "Testing the concavity of an ordinaldominance curve," University of California at San Diego, Economics Working Paper Series qt6qg1f8ms, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt6qg1f8ms
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    1. Beare, Brendan K., 2011. "Measure preserving derivatives and the pricing kernel puzzle," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 689-697.
    2. Christopher A. Carolan & Joshua M. Tebbs, 2005. "Nonparametric tests for and against likelihood ratio ordering in the two-sample problem," Biometrika, Biometrika Trust, vol. 92(1), pages 159-171, March.
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    Keywords

    Social and Behavioral Sciences; null hypothesis;

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