Mean Empirical Likelihood

Empirical likelihood methods are widely used in different settings to construct the confidence regions for parameters which satisfy the moment constraints. However, the empirical likelihood ratio confidence regions may have poor accuracy, especially for small sample sizes and multi-dimensional situations. A novel Mean Empirical Likelihood (MEL) method is proposed. A new pseudo dataset using the means of observation values is constructed to define the empirical likelihood ratio and it is proved that this MEL ratio satisfies Wilks’ theorem. Simulations with different examples are given to assess its finite sample performance, which shows that the confidence regions constructed by Mean Empirical Likelihood are much more accurate than that of the other Empirical Likelihood methods.