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On the Consistency of Approximate Maximizing Estimator Sequences in the Case of Quasiconcave Functions

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  • Kemp, GCR

Abstract

This paper demonstrates consistency for estimators obtained by approximately maximizing a sequence of stochastic quasiconcave functions on RP that converges in probability pointwise to a non-stochastic function. In the scalar parameter case all that is necessary for consistency is that the parameter value of interest is a unique maximizer of the limiting function. However, in the vector parameter case certain further conditions on the limiting function are necessary to establish consistency. The paper also discusses the relation of these results to existing results on the consistency of estimators obtained by approximately maximizing concave functions and to the concepts of hypoconvergence and epiconvergence.

Suggested Citation

  • Kemp, GCR, 2007. "On the Consistency of Approximate Maximizing Estimator Sequences in the Case of Quasiconcave Functions," Economics Discussion Papers 2879, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:2879
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    References listed on IDEAS

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    1. Peter Kall, 1986. "Approximation to Optimization Problems: An Elementary Review," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 9-18, February.
    2. Mihail Zervos, 1999. "On the Epiconvergence of Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 495-508, May.
    3. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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