Comment: improved local efficiency and double robustness.

Area of Science:

• Statistics
• Causal Inference
• Missing Data Analysis

Background:

• Missing data and causal inference present significant challenges in statistical modeling.
• Existing estimators aim for improved local efficiency but may have limitations.
• Rubin and van der Laan (2008) proposed novel estimators for these problems.

Purpose of the Study:

• To analyze the properties of estimators proposed by Rubin and van der Laan (2008).
• To compare these estimators with existing methods in specific statistical contexts.
• To extend the applicability of these estimators to scenarios involving propensity score estimation.

Main Methods:

• Comparative analysis of estimators in linear model settings.
• Investigation of robustness properties, specifically double robustness.
• Development of extensions for propensity score estimation in missing data models.

Main Results:

• The proposed estimators demonstrate agreement with established estimators under linear models.
• A specific version of the Rubin and van der Laan estimators is identified as doubly robust.
• An extension is proposed for situations where the propensity score requires estimation.

Conclusions:

• The Rubin and van der Laan estimators offer a valuable contribution to missing data and causal inference.
• The identified doubly robust properties enhance their reliability.
• The suggested extension broadens their practical utility in complex statistical analyses.