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Bootstrap-Based Inference for Cube Root Asymptotics

Journal: Econometrica

Date: 20200901

Author: Cattaneo, Matias D.; Jansson, Michael; Nagasawa, Kenichi

Abstract:
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.

Link: Google Scholar

Key Findings

Valid Bootstrap Method for Cube Root Asymptotics

Developed a new bootstrap-based distributional approximation method that restores consistency by modifying the shape of the criterion function

Performance Comparison

The proposed method achieves better coverage rates and shorter confidence intervals compared to standard bootstrap and m-out-of-n bootstrap methods

Wide Applicability

Method works effectively across multiple econometric estimators including maximum score, panel data, and machine learning applications

Coverage Rates Across Bootstrap Methods

  • Standard bootstrap shows poor coverage (~64%)
  • M-out-of-n bootstrap achieves better coverage but with wider intervals
  • Proposed method maintains close to 95% coverage rate

Confidence Interval Lengths

  • M-out-of-n bootstrap produces wider confidence intervals
  • Proposed method achieves shorter interval lengths while maintaining coverage
  • Results consistent across different simulation designs (DGP 1-3)

Method Performance Across Estimators

  • Successfully applied to maximum score estimation
  • Effective for panel data models
  • Applicable to machine learning classification problems

Contribution and Implications

  • First valid bootstrap-based method for cube root asymptotics that modifies objective function rather than sampling distribution
  • Provides practical inference tool for important econometric estimators previously lacking valid bootstrap procedures
  • Computationally simple implementation requiring only estimation of Hessian matrix

Data Sources

  • Coverage rates and confidence interval lengths based on Table I simulation results
  • Performance comparison charts constructed using data from Monte Carlo experiments with n=1000, B=2000 bootstrap replications
  • Method applications data derived from empirical examples in Sections 4.1-4.4