Department of Economics and Business Economics

Bootstrap-Based Inference for Cube Root Consistent Estimators

Publication: ResearchWorking paper

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  • Matias D. Cattaneo
    Matias D. CattaneoUniversity of Michigan
  • Michael Jansson
  • Kenichi Nagasawa
    Kenichi NagasawaUniversity of MichiganUnited States
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.
Original languageEnglish
Place of PublicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages21
StatePublished - 5 May 2017
SeriesCREATES Research Papers
Number2017-18

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