Spatial median depth-based robust adjusted empirical likelihood

Empirical likelihood (EL) based inference for parameters defined by general estimating equations of Qin and Lawless [(1994), ‘Empirical Likelihood and General Estimating Equations’, The Annals of Statistics, 22, 300–325] remains an active research topic. However, the performance of the EL method can be hindered by non-robustness and empty set problems. In this paper, we propose a robust adjusted empirical likelihood (RAEL) to address these two problems simultaneously. The resulting RAEL ratio statistic is shown to have inherited the asymptotic properties of both the robust empirical likelihood and the adjusted empirical likelihood. The finite-sample performance of the proposed method is illustrated by simulation and two real-data examples are also presented.