Robust empirical likelihood inference of longitudinal partially linear models with missing response

A robust empirical likelihood framework incorporating Huber score and inverse probability weighting is proposed to simultaneously handle outliers and missing data in longitudinal data analysis. Longitudinal data analysis is often complicated by outliers and missing data, which require careful methodological treatment. This paper proposes a robust empirical likelihood framework to address these issues in partially linear models for longitudinal data. By incorporating the bounded Huber score function, inverse probability weighting, and quadratic inference functions, we develop a robust empirical likelihood estimation procedure for regression parameter that simultaneously handles outliers and missing data while avoiding the need to estimate nuisance parameters in the working correlation matrix. Under mild regularity conditions, we establish the asymptotic properties of the robust empirical likelihood estimators and the corresponding log-likelihood ratio statistics. The effectiveness of the proposed method is demonstrated through some numerical simulations and a real data analysis.