Applications of Random Set Theory in Econometrics

Literature Cited

1. Andrews DWK, Shi X. 2013. Inference based on conditional moment inequalities. Econometrica 81:609–66 [Google Scholar]
2. Andrews DWK, Soares G. 2010. Inference for parameters defined by moment inequalities using generalized moment selection. Econometrica 78:119–57 [Google Scholar]
3. Artstein Z. 1983. Distributions of random sets and random selections. Isr. J. Math. 46:313–24 [Google Scholar]
4. Artstein Z, Vitale RA. 1975. A strong law of large numbers for random compact sets. Ann. Probab. 3:879–82 [Google Scholar]
5. Aubin J-P, Frankowska H. 1990. Set-Valued Analysis. Boston: Birkhäuser
6. Aumann RJ. 1965. Integrals of set-valued functions. J. Math. Anal. Appl. 12:1–12 [Google Scholar]
7. Bar HY, Molinari F. 2013. Computation of sets via data augmentation and support vector machines. Unpublished manuscript, Cornell Univ., Ithaca, NY
8. Beresteanu A, Molchanov I, Molinari F. 2011. Sharp identification regions in models with convex moment predictions. Econometrica 79:1785–821 [Google Scholar]
9. Beresteanu A, Molchanov I, Molinari F. 2012. Partial identification using random set theory. J. Econom. 166:17–32. Errata. http://econweb.arts.cornell.edu/fmolinari/NOTE_BMM2012_v3.pdf
10. Beresteanu A, Molinari F. 2008. Asymptotic properties for a class of partially identified models. Econometrica 76:763–814 [Google Scholar]
11. Berry ST, Tamer E. 2007. Identification in models of oligopoly entry. Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress Vol. II Blundell R, Newey WK, Persson T. 46–85 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
12. Bickel PJ, Klaassen CA, Ritov Y, Wellner JA. 1993. Efficient and Adaptive Estimation for Semiparametric Models New York: Springer
13. Bontemps C, Magnac T, Maurin E. 2012. Set identified linear models. Econometrica 80:1129–55 [Google Scholar]
14. Boyd S, Vandenberghe L. 2004. Convex Optimization Cambridge, UK: Cambridge Univ. Press
15. Chandrasekhar A, Chernozhukov V, Molinari F, Schrimpf P. 2012. Inference for best linear approximations to set identified functions. Work. Pap. CWP 43/12, CeMMAP, London
16. Chernozhukov V, Hong H, Tamer E. 2007. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75:1243–84 [Google Scholar]
17. Chernozhukov V, Kocatulum E, Menzel K. 2012. Inference on sets in finance. Work. Pap. CWP 46/12, CeMMAP, London
18. Chesher A, Rosen AM. 2012. Simultaneous equations models for discrete outcomes: coherence, completeness, and identification. Work. Pap. CWP21/12, CeMMAP, London
19. Chesher A, Rosen AM, Smolinski K. 2013. An instrumental variable model of multiple discrete choice. Quant. Econ. 4:157–96 [Google Scholar]
20. Choquet G. 1953/1954. Theory of capacities. Ann. Inst. Fourier 5:131–295 [Google Scholar]
21. Ciliberto F, Tamer E. 2009. Market structure and multiple equilibria in airline markets. Econometrica 77:1791–828 [Google Scholar]
22. Debreu G. 1967. Integration of correspondences. Proc. 5th Berkeley Symp. Math. Stat. Probab Vol. 2351–72 Berkeley: Univ. Calif. Press [Google Scholar]
23. Galichon A, Henry M. 2006. Inference in incomplete models. Unpublished manuscript, Columbia Univ., New York
24. Galichon A, Henry M. 2011. Set identification in models with multiple equilibria. Rev. Econ. Stud. 78:1264–98 [Google Scholar]
25. Gilboa I. 2004. Uncertainty in Economic Theory: Essays in Honor of David Schmeidler’s 65th Birthday London: Routledge
26. Grant M, Boyd S. 2010. CVX: Matlab software for disciplined convex programming, version 1.21. http://cvxr.com/cvx
27. Hartigan JA. 1975. Clustering Algorithms New York: Wiley
28. Hörmander L. 1954. Sur la fonction d’appui des ensembles convexes dans un espace localement convexe. Ark. Mat. 3:181–86 [Google Scholar]
29. Horowitz JL, Manski CF. 2000. Nonparametric analysis of randomized experiments with missing covariate and outcome data. J. Am. Stat. Assoc. 95:77–84 [Google Scholar]
30. Horowitz JL, Manski CF, Ponomareva M, Stoye J. 2003. Computation of bounds on population parameters when the data are incomplete. Reliab. Comput. 9:419–40 [Google Scholar]
31. Imbens GW, Manski CF. 2004. Confidence intervals for partially identified parameters. Econometrica 72:1845–57 [Google Scholar]
32. Kaido H. 2012. A dual approach to inference for partially identified econometric models. Work. Pap., Boston Univ.
33. Kaido H, Molinari F, Stoye J. 2013. Inference for projections of identified sets. Manuscript in preparation
34. Kaido H, Santos A. 2014. Asymptotically efficient estimation of models defined by convex moment inequalities. Econometrica 82:387–413 [Google Scholar]
35. Kolmogorov AN. 1950. Foundations of the Theory of Probability New York: Chelsea:
36. Manski CF. 1989. Anatomy of the selection problem. J. Hum. Resour. 24:343–60 [Google Scholar]
37. Manski CF. 1995. Identification Problems in the Social Sciences Cambridge, MA: Harvard Univ. Press
38. Manski CF. 2003. Partial Identification of Probability Distributions New York: Springer-Verlag
39. Manski CF, Tamer E. 2002. Inference on regressions with interval data on a regressor or outcome. Econometrica 70:519–46 [Google Scholar]
40. Mason DM, Polonik W. 2009. Asymptotic normality of plug-in level set estimates. Ann. Stat. 19:1108–42 [Google Scholar]
41. Matheron G. 1975. Random Sets and Integral Geometry New York: Wiley
42. Molchanov I. 1998. A limit theorem for solutions of inequalities. Scand. J. Stat. 25:235–42 [Google Scholar]
43. Molchanov I. 2005. Theory of Random Sets London: Springer
44. Molchanov I, Molinari F. 2014. Random Sets in Econometrics. In preparation
45. Molinari F. 2008. Partial identification of probability distributions with misclassified data. J. Econom. 144:81–117 [Google Scholar]
46. Norberg T. 1992. On the existence of ordered couplings of random sets: with applications. Isr. J. Math. 77:241–64 [Google Scholar]
47. Polonik W. 1995. Measuring mass concentrations and estimating density contour clusters: an excess mass approach. Ann. Stat. 23:855–81 [Google Scholar]
48. Rigollet P, Vert R. 2009. Optimal rates in plug-in estimators of density level sets. Bernoulli 15:1154–78 [Google Scholar]
49. Schneider R. 1993. Convex Bodies: The Brunn-Minkowski Theory Cambridge, UK: Cambridge Univ. Press
50. Tamer E. 2003. Incomplete simultaneous discrete response model with multiple equilibria. Rev. Econ. Stud. 70:147–65 [Google Scholar]
51. Tamer E. 2010. Partial identification in econometrics. Annu. Rev. Econ. 2:167–95 [Google Scholar]