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Consistency Of Plug-In Estimators Of Upper Contour And Level Sets

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  • Yildiz, Neşe

Abstract

This paper studies the problem of estimating the set of finite-dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This paper also suggests extremum estimators that with probability approaching 1 agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. In particular, it is shown that the set of minimizers of the sample generalized method of moments (GMM) objective function is consistent for the set of minimizers of the population GMM objective function in Hausdorff metric.

Suggested Citation

  • Yildiz, Neşe, 2012. "Consistency Of Plug-In Estimators Of Upper Contour And Level Sets," Econometric Theory, Cambridge University Press, vol. 28(02), pages 309-327, April.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:02:p:309-327_00
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    References listed on IDEAS

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    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, pages 525-574.
    2. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, pages 1193-1227.
    3. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    4. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, pages 345-357.
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    Cited by:

    1. Jason R. Blevins, 2013. "Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators," Working Papers 13-02, Ohio State University, Department of Economics.
    2. Arellano, Manuel & Hansen, Lars Peter & Sentana, Enrique, 2012. "Underidentification?," Journal of Econometrics, Elsevier, pages 256-280.
    3. David Martinez‐Miera & Rafael Repullo, 2017. "Search for Yield," Econometrica, Econometric Society, vol. 85, pages 351-378, March.
    4. Kaido, Hiroaki, 2016. "A dual approach to inference for partially identified econometric models," Journal of Econometrics, Elsevier, pages 269-290.

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