Doubly robust nonparametric inference on the average treatment effect

Area of Science:

• Statistics
• Causal Inference
• Econometrics

Background:

• Doubly robust (DR) estimators are crucial for causal inference, providing consistent estimates of average treatment effects under weaker conditions.
• Standard DR methods assume consistent estimation of nuisance parameters, which is often unmet with flexible, data-adaptive estimation techniques.

Purpose of the Study:

• To investigate the behavior of DR estimators when nuisance parameters are inconsistently estimated.
• To identify and evaluate methods for achieving doubly robust inference in the presence of estimation challenges.

Main Methods:

• Theoretical analysis of DR estimator properties under misspecified nuisance parameters.
• Comparison of different construction methods for DR estimators.
• Numerical simulations to assess practical performance.

Main Results:

• Targeted minimum loss-based estimation (TMLE) naturally extends to provide doubly robust inference even with inconsistent nuisance parameter estimation.
• Common alternative frameworks for constructing DR estimators are often inappropriate for achieving robust inference in this setting.

Conclusions:

• TMLE provides a viable and theoretically sound approach for robust causal effect estimation when nuisance parameters are estimated using flexible methods.
• The findings have broad implications for developing robust statistical inference methods in various fields beyond treatment effect estimation.