A novel approach of empirical likelihood with massive data

Statistical analysis of large datasets is a challenge because of the limitation of computing devices' memory and excessive computation time. Divide and Conquer (DC) algorithm is an effective solution path, but the DC algorithm still has limitations for statistical inference. Empirical likelihood is an important semiparametric and nonparametric statistical method for parameter estimation and statistical inference, and the estimating equation builds a bridge between empirical likelihood and traditional statistical methods, which makes empirical likelihood widely used in various traditional statistical models. In this paper, we propose a novel approach to address the challenges posed by empirical likelihood with massive data, which is called split sample mean empirical likelihood(SSMEL), our approach provides a unique perspective for sovling big data problem. We show that the SSMEL estimator has the same estimation efficiency as the empirical likelihood estimator with the full dataset, and maintains the important statistical property of Wilks' theorem, allowing our proposed approach to be used for statistical inference. The effectiveness of the proposed approach is illustrated using simulation studies and real data analysis.