• Corpus ID: 34119537

Bootstrap-Based Inference for Cube Root Consistent Estimators

@article{Cattaneo2017BootstrapBasedIF,
  title={Bootstrap-Based Inference for Cube Root Consistent Estimators},
  author={M. D. Cattaneo and Michael Jansson and Kenichi Nagasawa},
  journal={arXiv: Statistics Theory},
  year={2017}
}
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… 

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