Bootstrap-Based Inference for Cube Root Asymptotics

This paper proposes a consistent bootstrap-based distributional approximation for cube root consistent and related estimators exhibiting a Chernoff (1964)-type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is 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. We illustrate the applicability of our core idea with six canonical examples in statistics, machine learning, econometrics, and biostatistics. Simulation evidence is also provided.