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Published on: July 3, 2020
Nonparametric bootstrap inference for the targeted highly adaptive least absolute shrinkage and selection operator
Weixin Cai1, Mark van der Laan1
1Division of Biostatistics, University of California, Berkeley, USA.
The Highly-Adaptive LASSO Targeted Minimum Loss Estimator (HAL-TMLE) uses nonparametric bootstrap for consistent estimation. A novel method optimizes confidence intervals by selecting the sectional variation norm for better finite sample coverage.
Area of Science:
- Statistics
- Machine Learning
Background:
- The Highly-Adaptive LASSO Targeted Minimum Loss Estimator (HAL-TMLE) is an efficient estimator for pathwise differentiable parameters.
- It assumes finite sectional variation norm of nuisance functions, using HAL-MLE for initial estimation with cross-validation for norm selection.
Purpose of the Study:
- To establish the consistency of the nonparametric bootstrap for HAL-TMLE.
- To propose a method for optimizing finite sample coverage of bootstrap confidence intervals by selecting the sectional variation norm.
Main Methods:
- Establishing nonparametric bootstrap consistency for HAL-TMLE with a fixed sectional variation norm.
- Proposing a selection method for the sectional variation norm based on bootstrap confidence interval width plateau.
- Demonstrating the method on average treatment effect and multivariate density estimation.
Main Results:
- The nonparametric bootstrap is a consistent method for estimating the normal limit distribution of HAL-TMLE.
- The proposed selection method optimizes the finite sample coverage of bootstrap confidence intervals.
- Simulation results show excellent finite sample coverage for bootstrap-based confidence intervals in demonstrated examples.
Conclusions:
- The nonparametric bootstrap provides a reliable method for HAL-TMLE inference.
- The proposed sectional variation norm selection enhances the practical utility of bootstrap confidence intervals.
- The methods are effective for complex nonparametric estimation tasks.
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