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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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    Cited by:

    1. Isaiah Andrews & Jonathan Roth & Ariel Pakes, 2023. "Inference for Linear Conditional Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(6), pages 2763-2791.
    2. Jun, Sung Jae & Pinkse, Joris, 2024. "An information–Theoretic approach to partially identified auction models," Journal of Econometrics, Elsevier, vol. 238(2).
    3. Paul S. Koh, 2022. "Estimating Discrete Games of Complete Information: Bringing Logit Back in the Game," Papers 2205.05002, arXiv.org, revised Aug 2024.
    4. Roy Allen & Paweł Dziewulski & John Rehbeck, 2024. "Revealed statistical consumer theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(3), pages 823-847, May.
    5. Bryan S. Graham & Geert Ridder & Petra Thiemann & Gema Zamarro, 2023. "Teacher-to-Classroom Assignment and Student Achievement," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1328-1340, October.
    6. Luofeng Liao & Christian Kroer, 2023. "Statistical Inference and A/B Testing for First-Price Pacing Equilibria," Papers 2301.02276, arXiv.org, revised Jun 2023.
    7. Paul S. Willen & David Hao Zhang, 2020. "Do Lenders Still Discriminate? A Robust Approach for Assessing Differences in Menus," Working Papers 20-19, Federal Reserve Bank of Boston.
    8. Sarah Moon, 2024. "Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model," Papers 2403.07236, arXiv.org, revised May 2024.
    9. Luofeng Liao & Christian Kroer, 2024. "Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium," Papers 2402.02303, arXiv.org, revised Feb 2024.
    10. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    11. Luofeng Liao & Christian Kroer, 2024. "Statistical Inference and A/B Testing in Fisher Markets and Paced Auctions," Papers 2406.15522, arXiv.org, revised Aug 2024.
    12. Han, Sukjin & Yang, Shenshen, 2024. "A computational approach to identification of treatment effects for policy evaluation," Journal of Econometrics, Elsevier, vol. 240(1).
    13. Allen, Roy & Dziewulski, Paweł & Rehbeck, John, 2022. "Making sense of monkey business: Re-examining tests of animal rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 220-228.
    14. Zach Flynn, 2020. "Identifying productivity when it is a factor of production," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 496-530, June.
    15. Fu Ouyang & Thomas T. Yang, 2023. "Semiparametric Discrete Choice Models for Bundles," Papers 2306.04135, arXiv.org, revised Nov 2023.
    16. Wenlong Ji & Lihua Lei & Asher Spector, 2023. "Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects," Papers 2310.08115, arXiv.org, revised Nov 2024.
    17. Luther Yap, 2022. "Sensitivity of Policy Relevant Treatment Parameters to Violations of Monotonicity," Working Papers 655, Princeton University, Department of Economics, Industrial Relations Section..

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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