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Differential Imaging of Biological Structures with Doubly-resonant Coherent Anti-stokes Raman Scattering CARS

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Doubly robust nonparametric inference on the average treatment effect.

D Benkeser¹, M Carone², M J Van Der Laan³

¹Department of Biostatistics and Bioinformatics, Emory University, 1518 Clifton Rd NE, Atlanta, Georgia 30322, U.S.A.benkeser@emory.edu.

|February 13, 2018

Summary

This summary is machine-generated.

Doubly robust estimators for treatment effects can fail when nuisance parameters are estimated flexibly. Targeted minimum loss-based estimation offers a robust solution for valid statistical inference in these challenging scenarios.

Keywords:

Adaptive estimation Doubly robust estimation Efficient influence function Targeted minimum loss-based estimation

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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.