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

Jason Blevins ()

No 13-02, Working Papers from Ohio State University, Department of Economics

Abstract: 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.

Keywords: partial identification; cube-root asymptotics; semiparametric models; limited support regressors; transformation model; binary response model; maximum score estimator (search for similar items in EconPapers)
JEL-codes: C13 C14 C25 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2013-12
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