Three Methods of Empirical Euclidean Likelihood for Two Sample and Their Comparison

This paper studies the three methods of empirical Euclidean likelihood for two sample: empirical Euclidean likelihood based on two unbiased estimating functions; empirical Euclidean penalized likelihood based on an unbiased estimating function and an empirical estimator; weighted sum based on two empirical estimators. The strong consistency, asymptotic normality and asymptotic efficiency of these methods are proved. The results show that asymptotic efficiency of each of the three methods is the same.