Distributed Empirical Likelihood Estimation In Massive Data

When the sample size becomes quite large or the data are stored in a distributed manner,traditional statistical inference will be infeasible due to time consuming,memory limitations,communication cost and privacy concerns.This paper proposes two distributed estimators called divide-and-conquer empirical likelihood(DEL)and divide-and-conquer exponentially tilted empirical likelihood(DETEL)for estimating equations in the presence of massive data.In addition,we derive upper bounds for mean squared error of DEL and DETEL estimators,and establish the theoretical properties for them under mild conditions.The results show that the oracle properties of proposed estimators are the same as those of EL and ETEL estimators with appropriate condition of ,which is the number of groups of sample after dividing.Finally,a lot of numerical simulation studies and real data analysis are carried to verify the superiority of our proposed distributed estimators.Simulation results show that the proposed distributed estimators have dramatically shorted running time and don't significantly diverge with the centralized estimators obtained via the full dataset under mean squared error.