Statistical Inferences for Missing Response Problems Based on Modified Empirical Likelihood

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Missing data poses significant challenges in statistical inference.
• Empirical likelihood (EL) is a powerful, non-parametric method for statistical inference.
• Existing EL methods have limitations in parameter hypothesis testing and handling missing responses.

Purpose of the Study:

• To modify and advance the empirical likelihood (EL) approach for statistical inference with missing response data.
• To develop consistent mean estimators and confidence intervals for data with missing responses.
• To extend EL methods for estimating average treatment effects in causal inference.

Main Methods:

• Modified the empirical likelihood (EL) approach to address missing response data.
• Developed consistent mean estimators and confidence intervals.
• Extended EL for estimating average treatment effect (ATE) in causal inference settings.
• Proved the consistency of the proposed ATE estimators.

Main Results:

• Proposed consistent mean estimators and confidence intervals for missing response data.
• Developed analogous estimators for average treatment effect (ATE).
• Demonstrated the utility of the estimators in a real-world causal inference scenario.
• Simulations showed the proposed estimators outperform historical methods in terms of relative Root Mean Squared Error (RMSE) and coverage probability.

Conclusions:

• The enhanced empirical likelihood (EL) approach provides effective statistical inference for missing response data.
• The proposed methods offer improved accuracy and reliability in estimating mean responses and average treatment effects.
• This work advances the application of EL in challenging statistical and causal inference problems.