Composite quantile regression based robust empirical likelihood for partially linear spatial autoregressive models

In this paper, we consider the robust estimation for a class of partially linear spatial autoregressive models. By combining empirical likelihood and composite quantile regression methods, we propose a robust empirical likelihood estimation procedure. Under some regularity conditions, the proposed empirical log-likelihood ratio is proved to be asymptotically chi-squared, and the convergence rate of the estimator for nonparametric component is also derived. Some simulation analyses are conducted for further illustrating the performance of the proposed method, and simulation results show that the proposed method is more robust.