School of Mathematics and Statistics, Guangxi Normal University; Kaifeng Vocational College of Culture and Arts

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.