A Generally Efficient Targeted Minimum Loss Based Estimator based on the Highly Adaptive Lasso.

Area of Science:

• Statistics
• Machine Learning
• Causal Inference

Background:

• Efficient estimation of target parameters in statistical models is crucial for reliable inference.
• Existing methods for targeted minimum loss-based estimation (TMLE) rely on accurate estimation of nuisance parameters.
• The properties of nuisance parameters, particularly their smoothness and variation, impact the efficiency of TMLE.

Purpose of the Study:

• To construct an efficient targeted minimum loss-based estimator (TMLE) for pathwise differentiable target parameters.
• To develop a new minimum loss-based estimator for nuisance parameters with improved convergence rates.
• To demonstrate the asymptotic efficiency of a one-step TMLE using the proposed estimator in a causal inference setting.

Main Methods:

• Introduced the highly adaptive Lasso (HAL)-estimator, a constrained empirical risk minimizer for nuisance parameters.
• Utilized cross-validation to select the constraint constant for the HAL-estimator's variation norm.
• Incorporated the HAL-estimator into an ensemble super-learner and applied it in a one-step TMLE framework.

Main Results:

• The HAL-estimator converges to the true nuisance parameter value at a rate faster than n^(-1/4).
• Super-learners utilizing the HAL-estimator achieve rates asymptotically equivalent to oracle estimators.
• The proposed one-step TMLE is asymptotically efficient for any data-generating distribution under weak structural conditions and positivity assumptions.

Conclusions:

• The HAL-estimator provides a significant improvement in nuisance parameter estimation for TMLE.
• The developed TMLE framework ensures asymptotic efficiency in complex statistical models, including causal effect estimation.
• This work advances the practical application of efficient and robust statistical estimation techniques.