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Empirical likelihood is a very important nonparametric approach which is ofwide application. However, it is hard and even infeasible to calculate theempirical log-likelihood ratio statistic with massive data. The main challengeis the calculation of the Lagrange multiplier. This motivates us to develop adistributed empirical likelihood method by calculating the Lagrange multiplierin a multi-round distributed manner. It is shown that the distributed empiricallog-likelihood ratio statistic is asymptotically standard chi-squared undersome mild conditions. The proposed algorithm is communication-efficient andachieves the desired accuracy in a few rounds. Further, the distributedempirical likelihood method is extended to the case of Byzantine failures. Amachine selection algorithm is developed to identify the worker machineswithout Byzantine failures such that the distributed empirical likelihoodmethod can be applied. The proposed methods are evaluated by numericalsimulations and illustrated with an analysis of airline on-time performancestudy and a surface climate analysis of Yangtze River Economic Belt.

Distributed Empirical Likelihood Inference With or Without Byzantine Failures