Robust estimation and bias-corrected empirical likelihood in generalized linear models with right censored data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Generalized linear models (GLMs) are widely used but sensitive to outliers and censoring.
• Robust methods are needed for reliable regression parameter estimation in the presence of data anomalies.
• Empirical likelihood offers a non-parametric approach to inference, but requires adjustments for censored data.

Purpose of the Study:

• To develop robust estimation techniques for regression parameters in GLMs with right-censored data.
• To construct a bias-corrected empirical likelihood ratio statistic for accurate confidence region estimation.
• To propose a method for selecting tuning parameters in the loss function for robust estimation.

Main Methods:

• A robust estimating equation is proposed for regression parameter estimation.
• A bias-corrected empirical log-likelihood ratio statistic is developed and its weak convergence is established.
• A novel method for tuning parameter selection in the loss function is introduced.

Main Results:

• The proposed robust estimator is consistent and asymptotically normal.
• The bias-corrected empirical log-likelihood ratio statistic converges weakly to a standard distribution, enabling direct confidence region construction.
• Simulation studies demonstrate the robustness of the estimator and the superiority of the bias-corrected empirical likelihood over normal approximation.

Conclusions:

• The developed robust estimation and bias-corrected empirical likelihood methods are effective for GLMs with right-censored data.
• The proposed techniques offer improved accuracy and reliability for regression parameter inference.
• The methods are applicable to real-world problems, as demonstrated by an Alzheimer's disease dataset analysis.