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A Karush-Kuhn-Tucker test of convexity for univariate observations


  • Sofia Georgiadou

    (University of Athens)

  • Ioannis C. Demetriou

    () (University of Athens)


The problem of convexity runs deeply in economic theory. For example, increasing returns or upward slopes (convexity) and diminishing returns or downward slopes (concavity) of certain supply, demand, production and utility relations are often assumed in economics. Quite frequently, however, the observations have lost convexity (or concavity) due to errors of the measuring process. We derive the Karush-Kuhn-Tucker test statistic of convexity, when the estimator of the data minimizes the sum of squares of residuals subject to the assumption of non-decreasing returns. It is a highly structured quadratic programming problem that allows a very efficient calculation of the test statistic. Certain applications that test the convexity assumption of real economic data are considered and the interpretation capability of the test is demonstrated. Some numerical results illustrate the computation and present the efficacy of the test in small, medium and large data sets. They suggest that the test is suitable when the number of observations is very large

Suggested Citation

  • Sofia Georgiadou & Ioannis C. Demetriou, 2006. "A Karush-Kuhn-Tucker test of convexity for univariate observations," Computing in Economics and Finance 2006 435, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:435

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    More about this item


    convexity; data fitting; diminishing return; least squares;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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