Distributed estimation with empirical likelihood

With the development of science and technology, massive datasets stored in multiple machines are increasingly prevalent. It is known that traditional statistical methods may be infeasible for analyzing large datasets owing to excessive computing time, memory limitations, communication costs, and privacy concerns. This article develops divide-and-conquer empirical likelihood (DEL) and divide-and-conquer exponentially tilted empirical likelihood (DETEL) methods for the distributed computing setting. We investigate the theoretical properties of the DEL and DETEL estimators. In particular, we derive upper bounds for the mean squared errors of the DEL and DETEL estimators, and, under some mild conditions, we prove the consistency and the asymptotic normality of the proposed estimators. Simulation studies and a real data analysis are carried out to demonstrate the finite-sample performance of the proposed methods.