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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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摘要 经验似然方法自提出以来, 得到了广泛的应用. 但是, 经验似然方法也存在一些问题, 特别是在样本量较小时覆盖率较低. 针对这个问题, 以往文献中有许多讨论.本文用全新的数据处理方法来解决这个问题, 这个方法称为平均经验似然方法. 它的基本想法就是将原始数据两两平均, 然后用新的数据集来构造经验似然比统计量. 本文证明新构造的平均经验似然比统计量仍然满足Wilks 性质, 而且容易推广. 随机模拟表明, 新方法计算简单快速, 与以往方法相比较, 新方法所构造的置信区间覆盖率大大提高.
关键词 经验似然方法平均经验似然    
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  
基金资助:国家自然科学基金 (Nos. 11171230, 11231010, 11471272).
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[3] DiCiccio, T., Hall, P. and Romano, J., Empirical likelihood is Bartlett-correctable, Ann. Statist., 1991, 19(2): 1053-1061.
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[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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