Balanced Augmented Empirical Euclidean Likelihood

Empirical (Euclidean) likelihood is a very popular nonparametric statistical method in recent years. In view of the convex hull restrictions and complex calculation of empirical (Euclidean) likelihood, the balanced augmented empirical Euclidean likelihood (BAEEL) is proposed by using the idea of Emerson and Owen (2009). Then the BAEEL method is investigated from two aspects of theory and simulation. In theory, the connection between BAEEL method and the empirical Euclidean likelihood method is deduced. That is, with fixed sample size and the continuous varied location of augmented points, the test can be varied from the simple mean augmented empirical Euclidean likelihood to empirical Euclidean likelihood test. Simulation results show that the distribution of the BAEEL converges its limit distribution more rapidly than that of the (adjusted) empirical Euclidean likelihood in most cases.