Robust confidence regions for the semi-parametric regression model with responses missing at random

In this paper, a regression semi-parametric model is considered where responses are assumed to be missing at random. From the empirical likelihood function defined based on the rank-based estimating equation, robust confidence intervals/regions of the true regression coefficient are derived. Monte Carlo simulation experiments show that the proposed approach provides more accurate confidence intervals/regions compared to its normal approximation counterpart under different model error structure. The approach is also compared with the least squares approach, and its superiority is shown whenever the error distribution in the simulation study is heavy tailed or contaminated. Finally, a real data example is given to illustrate our proposed method.