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Non-Standard Rates of Convergence of Criterion-Function-Based Set Estimators

  • Jason R. Blevins

    ()

    (Department of Economics, Ohio State University)

This paper establishes conditions for consistency and potentially non-standard rates of convergence for set estimators based on contour sets of criterion functions. These conditions cover the standard parametric rate $n^{-1/2}$, non-standard polynomial rates such as $n^{-1/3}$, and an extreme case of arbitrarily fast convergence. We also establish the validity of a subsampling procedure for constructing confidence sets for the identified set. We then provide more convenient sufficient conditions on the underlying empirical processes for cube root convergence. We show that these conditions apply to a class of transformation models under weak semiparametric assumptions which may be partially identified due to potentially limited-support regressors. We focus in particular on a semiparametric binary response model under a conditional median restriction and show that a set estimator analogous to the maximum score estimator is essentially cube-root consistent for the identified set when a continuous but possibly bounded regressor is present. Arbitrarily fast convergence occurs when all regressors are discrete. Finally, we carry out a series of Monte Carlo experiments which verify our theoretical findings and shed light on the finite sample performance of the proposed procedures.

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File URL: http://www.econ.ohio-state.edu/pdf/blevins/wp13-02.pdf
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Paper provided by Ohio State University, Department of Economics in its series Working Papers with number 13-02.

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Length: 45 Pages
Date of creation: Dec 2013
Date of revision:
Handle: RePEc:osu:osuewp:13-02
Contact details of provider: Postal: 410 Arps Hall 1945 North High Street Columbus, Ohio 43210-1172

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  1. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-62, March.
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  7. Donald W.K. Andrews & Xiaoxia Shi, 2011. "Nonparametric Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1840RR, Cowles Foundation for Research in Economics, Yale University, revised Oct 2013.
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  11. Thierry Magnac & Eric Maurin, 2004. "Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data," Working Papers 2004-11, Centre de Recherche en Economie et Statistique.
  12. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
  13. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
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  26. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
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