Empirical likelihood-based inference for the difference of two location parameters using smoothed M-estimators We consider one of the classical problems in statistics: the inference for the two-sample location problem. In this paper, we present a new empirical likelihood (EL) method for the difference of two smoothed M-estimators. To deal with additional nuisance scale parameters, we use the plug-in empirical likelihood, and we establish asymptotic properties of the new estimators. For the empirical study, we consider the important case of the smoothed Huber M-estimator. Our empirical results show that the new method is a competitive alternative to the classical procedures regarding inference about the difference of two location parameters. The software implementation for the new empirical likelihood method is based on the R package extit{EL}, which has been developed for related two-sample problems.

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