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Finite Sample Inference in Incomplete Models

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  • Lixiong Li
  • Marc Henry

Abstract

We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test statistic is a discrete analogue of a new optimal transport characterization of the sharp identified region. Both test statistic and critical values rely on simulation drawn from the distribution of latent variables and are computed using solutions to discrete optimal transport, hence linear programming problems. We also propose a fast preliminary search in the parameter space with an alternative, more conservative yet consistent test, based on a parameter free critical value.

Suggested Citation

  • Lixiong Li & Marc Henry, 2022. "Finite Sample Inference in Incomplete Models," Papers 2204.00473, arXiv.org.
    • Handle: RePEc:arx:papers:2204.00473
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    References listed on IDEAS

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    1. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    2. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
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    13. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
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    Cited by:

    1. Lujie Zhou, 2024. "Efficient Computation of Confidence Sets Using Classification on Equidistributed Grids," Papers 2401.01804, arXiv.org.

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