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Articles

Inference in a Class of Optimization Problems: Confidence Regions and Finite Sample Bounds on Errors in Coverage Probabilities

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References

  • Angrist, J. D., and Evans, W. N. (1998), “Children and their Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size,” American Economic Review, 88, 450–477.
  • Belloni, A., Bugni, F., and Chernozhukov, V. (2018), “Subvector Inference in Partially Identified Models with Many Moment Inequalities,” arXiv: 1806.11466 [math.ST]. Available at https://arxiv.org/abs/1806.11466.
  • Bentkus, V. (2003), “On the Dependence of the Berry–Esseen Bound on Dimension,” Journal of Statistical Planning and Inference, 113, 385–402. DOI: 10.1016/S0378-3758(02)00094-0.
  • Bertsimas, D., King, A., and Mazumder, R. (2016), “Best Subset Selection via a Modern Optimization Lens,” Annals of Statistics, 44, 813–852.
  • Blundell, R., Duncan, A., and Meghir, C. (1998), “Estimating Labor Supply Responses Using Tax Reforms,” Econometrica, 66, 827–861. DOI: 10.2307/2999575.
  • Bugni, F. A., Canay, I. A., and Shi, X. (2017). “Inference for Subvectors and other Functions of Partially Identified Parameters in Moment Inequality Models,” Quantitative Economics, 8, 1–38. DOI: 10.3982/QE490.
  • Bühlmann, P., and van de Geer, S. (2011), Statistics for High-Dimensional Data: Methods, Theory and Applications, Berlin: Springer.
  • Canay, I. A., and Shaikh, A. M. (2017), “Practical and Theoretical Advan- ces in Inference for Partially Identified Models,” in Advances in Economics and Econometrics: Eleventh World Congress, vol. 2 of Econometric Society Monographs, eds. B. Honoré, A. Pakes, M. Piazzesi, and L. Samuelson, pp. 271–306, Cambridge: Cambridge University Press.
  • Chen, X., Christensen, T. M., and Tamer, E. (2018), “Monte Carlo Confidence Sets for Identified Sets,” Econometrica, 86, 1965–2018. DOI: 10.3982/ECTA14525.
  • Chernozhukov, V., Chetverikov, D., and Kato, K. (2017), “Central Limit Theorems and Bootstrap in High Dimensions,” Annals of Probability, 45, 2309–2352.
  • Chernozhukov, V., Chetverikov, D., and Kato, K. (2019), “Inference on Causal and Structural Parameters using Many Moment Inequalities,” Review of Economic Studies, 86, 1867–1900.
  • Chernozhukov, V., Hansen, C., and Jansson, M. (2009), “Finite Sample Inference for Quantile Regression Models,” Journal of Econometrics, 152, 93–103. DOI: 10.1016/j.jeconom.2009.01.004.
  • Ciliberto, F., and Tamer, E. (2009), “Market Structure and Multiple Equilibria in Airline Markets,” Econometrica, 77, 1791–1828.
  • Clopper, C. J., and Pearson, E. S. (1934), “The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial,” Biometrika, 26, 404–413. DOI: 10.1093/biomet/26.4.404.
  • Freyberger, J., and Horowitz, J. L. (2015), “Identification and Shape Restrictions in Nonparametric Instrumental Variables Estimation,” Journal of Econometrics, 189, 41–53. DOI: 10.1016/j.jeconom.2015.06.020.
  • Ho, K., and Pakes, A. (2014), “Hospital Choices, Hospital Prices, and Financial Incentives to Physicians,” American Economic Review, 104, 3841–3884. DOI: 10.1257/aer.104.12.3841.
  • Ho, K., and Rosen, A. M. (2017), “Partial Identification in Applied Research: Benefits and Challenges,” in Advances in Economics and Econometrics: Eleventh World Congress, vol. 2 of Econometric Society Monographs, eds. B. Honoré, A. Pakes, M. Piazzesi, and L. Samuelson, pp. 307–359, Cambridge: Cambridge University Press.
  • Horowitz, J. L., and Lee, S. (2017), “Nonparametric Estimation and Inference under Shape Restrictions,” Journal of Econometrics, 201, 108–126. DOI: 10.1016/j.jeconom.2017.06.019.
  • Hsieh, Y.-W., Shi, X., and Shum, M. (2017), “Inference on Estimators defined by Mathematical Programming,” arXiv:1709.09115 [econ.EM], Available at https://arxiv.org/abs/1709.09115.
  • Hsu, D., Kakade, S., and Zhang, T. (2012), “A Tail Inequality for Quadratic Forms of SubGaussian Random Vectors,” Electronic Communications in Probability, 17, 1–6. DOI: 10.1214/ECP.v17-2079.
  • Kaido, H., Molinari, F., and Stoye, J. (2019), “Confidence Intervals for Projections of Partially Identified Parameters,” Econometrica, 87, 1397–1432. DOI: 10.3982/ECTA14075.
  • Kline, B., and Tamer, E. (2016), “Bayesian Inference in a Class of Partially Identified Models,” Quantitative Economics, 7, 329–366. DOI: 10.3982/QE399.
  • Kline, P., and Tartari, M. (2016), “Bounding the Labor Supply Responses to a Randomized Welfare Experiment: A Revealed Preference Approach,” American Economic Review, 106, 972–1014. DOI: 10.1257/aer.20130824.
  • Manski, C. F. (2007a), Identification for Prediction and Decision, Cambridge, MA: Harvard University Press.
  • Manski, C. F. (2007b), “Partial Identification of Counterfactual Choice Probabilities,” International Economic Review, 48, 1393–1410.
  • Minsker, S. (2015), “Geometric Median and Robust Estimation in Banach Spaces,” Bernoulli, 21, 2308–2335. DOI: 10.3150/14-BEJ645.
  • Molinari, F. (2020), “Microeconometrics with Partial Identification,” arXiv:2004.11751 [econ.EM]. Available at https://arxiv.org/abs/2004.11751.
  • Raič, M. (2019): “A multivariate Berry-Esseen theorem with explicit constants,” Bernoulli, 25(4A), 2824–2853. DOI: 10.3150/18-BEJ1072.
  • Reguant, M. (2016), “Bounding Outcomes in Counterfactual Analysis,” Northwestern University Working Paper.
  • Rosen, A. M., and Ura, T. (2019): “Finite Sample Inference for the Maximum Score Estimand,” arXiv:1903.01511 [econ.EM]. Available at https://arxiv.org/abs/1903.01511.
  • Ruggles, S., Flood, S., Foster, S., Goeken, R., Pacas, J., Schouweiler, M., and Sobek, M. (2021), “IPUMS USA: Version 11.0 [dataset],” Minneapolis, MN. DOI: 10.18128/D010.V11.0..
  • Shi, X., and Shum, M. (2015), “Simple Two-stage Inference for a Class of Partially Identified Models,” Econometric Theory, 31, 493–520. DOI: 10.1017/S0266466614000425.
  • Spokoiny, V., and Zhilova, M. (2015), “Bootstrap Confidence Sets under Model Misspecification,” Annals of Statistics, 43, 2653–2675.
  • Syrgkanis, V., Tamer, E., and Ziani, J. (2018), “Inference on Auctions with Weak Assumptions on Information,” arXiv:1710.03830 [econ.EM], Available at https://arxiv.org/abs/1710.03830.
  • Tamer, E. (2010), “Partial Identification in Econometrics,” Annual Review of Economics, 2, 167–195. DOI: 10.1146/annurev.economics.050708.143401.
  • Vershynin, R. (2018), High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge: Cambridge University Press.
  • Wainwright, M. J. (2019), High-dimensional Statistics: A Non-Asymptotic Viewpoint, Cambridge: Cambridge University Press.
  • Zhilova, M. (2020), “Nonclassical Berry-Esseen Inequalities and Accuracy of the Bootstrap,” Annals of Statistics, 48, 1922–1939.

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