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 数学进展 - 2018, Vol. 47(2): 287-295
 研究论文
 平均经验似然方法 Mean Empirical Likelihood 梁薇1,*,何书元2 LIANG Wei1, HE Shuyuan2 1. 厦门大学数学科学学院, 厦门, 福建, 361005; 2. 首都师范大学数学科学学院, 北京, 100048 1. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, P. R. China; 2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China 出版日期: 2018-05-16 2018, Vol. 47(2): 287-295 DOI: 10.11845/sxjz.2016088b
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Abstract：Empirical likelihood (EL) has been widely applied in many different occasions. However, there are still some problems in empirical likelihood method,such as that empirical likelihood ratio confidence regions may have poor accuracy, especially in small sample and multidimensional situations.There are a lot of discussions in the literature to solve this problem. In this paper, we introduce a so-called mean empirical likelihood (MEL) method to improve the EL accuracy. The basic idea of the MEL is to average each two original data to get an augmented data set, then with this augmented data set to construct the empirical likelihood ratio statistic, which is called MEL ratio statistics. We show that the MEL ratio statistic still satisfies the Wilks' theory, and it is extremely simple to use in practice. Simulation results show that the MEL method is simple and rapid, and compared with the previous EL methods, it is much more accurate.
Key wordsempirical likelihood    mean empirical likelihood
 PACS: O212.7

 [1] Chen, J.H., Variyath, A.M. and Abraham, B., Adjusted empirical likelihood and its properties, J. Comput. Graph. Stat., 2008, 17(2): 426-443.[2] Chen, S.X., On the accuracy of empirical likelihood confidence regions for linear regression model, Ann. Inst. Statist. Math., 1993, 45(4): 621-637.[3] DiCiccio, T., Hall, P. and Romano, J., Empirical likelihood is Bartlett-correctable, Ann. Statist., 1991, 19(2): 1053-1061.[4] Liu, Y.K. and Chen, J.H., Adjusted empirical likelihood with high-order precision, Ann. Statist., 2010, 38(3): 1341-1362.[5] Owen, A.B., Empirical likelihood ratio confidence regions, Ann. Statist., 1990, 18(1): 90-120.[6] Owen, A.B, Empirical Likelihood, London: Chapman & Hall, 2001.[7] Taso, M. and Wu, F., Empirical likelihood on the full parameter space, Ann. Statist., 2013, 41(4): 2176-2196.
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