Bootstrap-Based Inference for Cube Root Consistent Estimators

Matias Cattaneo, Michael Jansson and Kenichi Nagasawa ()
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Kenichi Nagasawa: University of Michigan, Postal: Department of Economics, University of Michigan

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This note proposes a consistent bootstrap-based distributional approximation for cube root consistent estimators such as the maximum score estimator of Manski (1975) and the isotonic density estimator of Grenander (1956). In both cases, the standard nonparametric bootstrap is known to be inconsistent. Our method restores consistency of the nonparametric bootstrap by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification leads to a generic and easy-to-implement resampling method for inference that is conceptually distinct from other available distributional approximations based on some form of modified bootstrap. We offer simulation evidence showcasing the performance of our inference method in finite samples. An extension of our methodology to general M-estimation problems is also discussed.

Keywords: Cube root asymptotics; Bootstrapping; Maximum score estimation; Isotonic density estimation. (search for similar items in EconPapers)
JEL-codes: C12 C14 C21 (search for similar items in EconPapers)
Pages: 21
Date: 2017-05-04
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Citations: View citations in EconPapers (5)

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