Inference under partial identification with minimax test statistics (2401.13057v2)
Abstract: We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in providing hypothesis tests under partial identification. Under general conditions, we provide an asymptotic characterization of such test statistics using the minimax theorem, and a means of computing critical values using the bootstrap. Making some light regularity assumptions, our results augment several asymptotic approximations that have been provided for partially identified hypothesis tests, and extend them by mitigating their dependence on local linear approximations of the parameter space. These asymptotic results are generally simple to state and straightforward to compute (esp.\ adversarially).
- Manifolds, Tensor Analysis, and Applications. Springer New York.
- Infinite Dimensional Analysis: A Hitchhiker’s Guide. Studies in Economic Theory. Springer.
- Inference based on conditional moment inequalities. Econometrica, 81(2):609–666.
- Wasserstein generative adversarial networks. In International conference on machine learning, pages 214–223. PMLR.
- Multiscale adaptive inference on conditional moment inequalities. Journal of Econometrics, 194(1):24–43.
- Baggett, L. (1991). Functional Analysis: A Primer. Chapman & Hall Pure and Applied Mathematics. Taylor & Francis.
- Convex Analysis and Nonlinear Optimization: Theory and Examples. CMS Books in Mathematics. Springer New York.
- Cheridito, P. (2013). Convex analysis. https://people.math.ethz.ch/~patrickc/CA2013.pdf.
- Intersection bounds: Estimation and inference. Econometrica, 81(2):667–737.
- Constrained conditional moment restriction models. Econometrica, 91(2):709–736.
- Chetverikov, D. (2018). Adaptive tests of conditional moment inequalities. Econometric Theory, 34(1):186–227.
- Conway, J. (1994). A Course in Functional Analysis. Graduate Texts in Mathematics. Springer New York.
- Deutsch, F. (2012). Best Approximation in Inner Product Spaces. CMS Books in Mathematics. Springer New York.
- Durrett, R. (2010). Probability: Theory and Examples. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 4 edition.
- Banach Space Theory: The Basis for Linear and Nonlinear Analysis. CMS Books in Mathematics. Springer New York.
- Partial identification and inference in moment models with incomplete data. Journal of Econometrics, 235(2):418–443.
- A projection framework for testing shape restrictions that form convex cones. Econometrica, 89(5):2439–2458.
- A practical guide to compact infinite dimensional parameter spaces. Econometric Reviews, 38(9):979–1006.
- Mathematical Analysis: Linear and Metric Structures and Continuity. Mathematical analysis. Birkhäuser Boston.
- Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50:1029–1054.
- Hong, S. (2017). Inference in semiparametric conditional moment models with partial identification. Journal of Econometrics, 196(1):156–179.
- An adversarial approach to structural estimation. Econometrica, 91(2041-2063).
- Advanced Calculus. Math Series. Jones and Bartlett Publishers.
- Instrumental variable estimation of nonparametric models. Econometrica, 51:1565–1578.
- Rockafellar, R. (1970). Convex Analysis. Princeton mathematical series. Princeton University Press.
- Rudin, W. (1976). Principles of Mathematical Analysis. International series in pure and applied mathematics. McGraw-Hill.
- Santos, A. (2012). Inference in nonparametric instrumental variables with partial identification. Econometrica, 80(1):213–275.
- Sargan, J. D. (1958). The estimation of economic relationships using instrumental variables. Econometrica, 26:393–415.
- Sion, M. (1958). On general minimax theorems. Pacific Journal of Mathematics, 8:171–176.
- Real Analysis. Princeton Lectures in Analysis. Princeton University Press.
- Tao, J. (2015). On the asymptotic theory for semi-nonparametric gmm models with partial identification.
- Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer-Verlag New York.
- Zhu, Y. (2020). Inference in nonparametric/semiparametric moment equality models with shape restrictions. Quantitative Economics, 11:609–636.
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