Empirical-likelihood-based confidence intervals for quantile regression models with longitudinal data

In this paper, we present three empirical likelihood (EL)-based inference procedures to construct confidence intervals for quantile regression models with longitudinal data. The traditional EL-based method suffers from an under-coverage problem, especially in small sample sizes. The proposed modified EL-based non-parametric methods including adjusted empirical likelihood (AEL), the transformed empirical likelihood (TEL), and the transformed adjusted empirical likelihood (TAEL) exhibit good finite sample performance over other existing procedures. Simulations are conducted to compare the performances of the proposed methods with the other methods in terms of coverage probabilities and average lengths of confidence intervals under different scenarios.