  This paper proposes a valid bootstrap-based distributional approximation for
M-estimators exhibiting a Chernoff (1964)-type limiting distribution. For
estimators of this kind, the standard nonparametric bootstrap is inconsistent.
The method proposed herein is based on the nonparametric bootstrap, but
restores consistency 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. We
illustrate the applicability of our results with four examples in econometrics
and machine learning.
