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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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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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