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Inference on Estimators defined by Mathematical Programming

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  • Yu-Wei Hsieh
  • Xiaoxia Shi
  • Matthew Shum

Abstract

We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both the objective function and the constraints of the mathematical programming problem may be estimated from data and hence involve sampling error. Our inference approach exploits the characterization of the solutions to these programming problems by complementarity conditions; by doing so, we can transform the problem of doing inference on the solution of a constrained optimization problem (a non-standard inference problem) into one involving inference based on a set of inequalities with pre-estimated coefficients, which is much better understood. We evaluate the performance of our procedure in several Monte Carlo simulations and an empirical application to the classic portfolio selection problem in finance.

Suggested Citation

  • Yu-Wei Hsieh & Xiaoxia Shi & Matthew Shum, 2017. "Inference on Estimators defined by Mathematical Programming," Papers 1709.09115, arXiv.org.
  • Handle: RePEc:arx:papers:1709.09115
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    File URL: http://arxiv.org/pdf/1709.09115
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    References listed on IDEAS

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    1. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    2. Xiaohong Chen & Timothy Christensen & Keith O'Hara & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2016.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. repec:wly:emetrp:v:86:y:2018:i:2:p:737-761 is not listed on IDEAS
    5. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    6. Guggenberger, Patrik & Hahn, Jinyong & Kim, Kyooil, 2008. "Specification testing under moment inequalities," Economics Letters, Elsevier, vol. 99(2), pages 375-378, May.
    7. Shi, Xiaoxia & Shum, Matthew, 2015. "Simple Two-Stage Inference For A Class Of Partially Identified Models," Econometric Theory, Cambridge University Press, vol. 31(03), pages 493-520, June.
    8. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
    9. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    10. Hiroaki Kaido & Andres Santos, 2014. "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities," Econometrica, Econometric Society, vol. 82(1), pages 387-413, January.
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