Empirical Likelihood for Random Sets

References

• Andrews, D. W. K., and Shi, X. (2015), “Inference Based on Conditional Moment Inequalities,” Econometrica, 81, 609–666.
   Web of Science ®Google Scholar
• Balke, A., and Pearl, J. (1997), “Bounds on Treatment Effects From Studies With Imperfect Compliance,” Journal of the American Statistical Association, 92, 1171–1176.
   Web of Science ®Google Scholar
• Beresteanu, A., Molchanov, I., and Molinari, F. (2012), “Partial Identification Using Random Set Theory,” Journal of Econometrics, 166, 17–32.
   Web of Science ®Google Scholar
• Beresteanu, A., and Molinari, F. (2008), “Asymptotic Properties for a Class of Partially Identified Models,” Econometrica, 76, 763–814.
   Web of Science ®Google Scholar
• Bontemps, C., Magnac, T., and Maurin, E. (2012), “Set Identified Linear Models,” Econometrica, 80, 1129–1155.
   Web of Science ®Google Scholar
• Canay, I. A. (2010), “EL Inference for Partially Identified Models: Large Deviations Optimality and Bootstrap Validity,” Journal of Econometrics, 156, 408–425.
   Web of Science ®Google Scholar
• Chan, N. H., Chen, S. X., Peng, L., and Yu, C. L. (2009), “Empirical Likelihood Methods Based on Characteristic Functions With Applications to Levy Processes,” Journal of the American Statistical Association, 104, 1621–1630.
   Web of Science ®Google Scholar
• Chandrasekhar, A., Chernozhukov, V., Molinari, F., and Schrimpf, P. (2012), “Inference for Best Linear Approximations to Set Identified Functions,” arXiv preprint arXiv:1212.5627.
   Google Scholar
• Chen, S. X., Härdle, W., and Li, M. (2003), “An Empirical Likelihood Goodness-of-Fit Test for Time Series,” Journal of the Royal Statistical Society, Series B, 65, 663–678.
   Google Scholar
• Chernozhukov, V., Kocatulum, E., and Menzel, K. (2015), “Inference on Sets in Finance,” Quantitative Economics, 6, 309–358.
   Web of Science ®Google Scholar
• Cressie, N., and Hulting, F. L. (1992), “A Spatial Statistical Analysis of Tumor Growth,” Journal of the American Statistical Association, 87, 272–283.
   Web of Science ®Google Scholar
• Donald, S. G., Imbens, G. W., and Newey, W. K. (2003), “Empirical Likelihood Estimation and Consistent Tests With Conditional Moment Restrictions,” Journal of Econometrics, 117, 55–93.
   Web of Science ®Google Scholar
• Fan, J., and Huang, L.-S. (2001), “Goodness-of-Fit Tests for Parametric Regression Models,” Journal of the American Statistical Association, 96, 640–652.
   Web of Science ®Google Scholar
• Fan, J., and Zhang, J. (2004), “Sieve Empirical Likelihood Ratio Tests for Nonparametric Functions,” Annals of Statistics, 32, 1858–1907.
   Web of Science ®Google Scholar
• Fan, J., Zhang, C., and Zhang, J. (2001), “Generalized Likelihood Ratio Statistics and Wilks Phenomenon,” Annals of Statistics, 29, 153–193.
   Web of Science ®Google Scholar
• Fisher, N. I., Hall, P., Turlach, B. A., and Watson, G. S. (1997), “On the Estimation of a Convex Set From Noisy Data on Its Support Function,” Journal of the American Statistical Association, 92, 84–91.
   Web of Science ®Google Scholar
• Giné, E., and Zinn, J. (1990), “Bootstrapping General Empirical Measures,” Annals of Probability, 18, 851–869.
   Web of Science ®Google Scholar
• Härdle, W., and Mammen, E. (1993), “Comparing Nonparametric Versus Parametric Regression Fits,” Annals of Statistics, 21, 1926–1947.
   Web of Science ®Google Scholar
• Hjort, N. L., McKeague, I. W. and van Keilegom, I. (2009), “Extending the Scope of Empirical Likelihood,” Annals of Statistics, 37, 1079–1111.
   Web of Science ®Google Scholar
• Horowitz, J. L., and Manski, C. F. (2000), “Nonparametric Analysis of Randomized Experiments With Missing Covariate and Outcome Data,” Journal of the American Statistical Association, 95, 77–84.
   Web of Science ®Google Scholar
• Kaido, H. (2012), A Dual Approach to Inference for Partially Identified Econometric Models,” Working Paper, Boston University.
   Google Scholar
• Kaido, H., and Santos, A. (2014), “Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities,” Econometrica, 82, 387–413.
   Web of Science ®Google Scholar
• Kendall, D. G. (1974), “Foundations of a Theory of Random Sets,” in Stochastic Geometry, eds. E. F. Harding, and D. G. Kendall, New York: Wiley, pp. 322–376.
   Google Scholar
• Lahiri, S. N. (1992), “Bootstrapping M-Estimators of a Multiple Linear Regression Parameter,” Annals of Statistics, 20, 1548–1570.
   Web of Science ®Google Scholar
• Li, G. (2003), “Nonparametric Likelihood Ratio Goodness-of-Fit Tests for Survival Data,” Journal of Multivariate Analysis, 86, 166–182.
   Web of Science ®Google Scholar
• Manski, C. F. (2003), Partial Identification of Probability Distributions, Berlin: Springer.
   Google Scholar
• Matheron, G. (1975), Random Sets and Integral Geometry, New York: Wiley.
   Google Scholar
• Molchanov, I. (2005), Theory of Random Sets.Berlin: Springer.
   Google Scholar
• Molchanov, I., and Molinari, F. (2014), “Applications of Random Set Theory in Econometrics,” Annual Review of Economics, 6, 229–251.
   Web of Science ®Google Scholar
• Owen, A. B. (2001), Empirical Likelihood, London: Chapman & Hall/CRC.
   Google Scholar
• Qin, J., and Lawless, J. (1994), “Empirical Likelihood and General Estimating Equations,” Annals of Statistics, 22, 300–325.
   Web of Science ®Google Scholar
• Shorack, G. (1982), “Bootstrapping Robust Regression,” Communications in Statistics: Theory and Methods, 11, 961–972.
   Web of Science ®Google Scholar
• Stoyan, D. (1998), “Random Sets: Models and Statistics,” International Statistical Review, 1998, 66, 1–27.
   Web of Science ®Google Scholar
• Stute, W. (1997), “Nonparametric Model Checks for Regression,” Annals of Statistics, 25, 613–641.
   Web of Science ®Google Scholar
• Stute, W., Gonzalez-Manteiga, W., and Quindimil, M. P. (1998), “Bootstrap Approximations in Model Checks for Regression,” Journal of the American Statistical Association, 93, 141–149.
   Web of Science ®Google Scholar
• Tamer, E. (2010), “Partial Identification in Econometrics,” Annual Review of Economics, 2, 167–195.
   Web of Science ®Google Scholar
• van der Vaart, A. W. (1998), Asymptotic Statistics, Cambridge, UK: Cambridge University Press.
   Google Scholar