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Empirical likelihood ratio under infinite second moment |
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| Authors: | Conghua Cheng Zhi Liu |
| Institution: | 1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, China;2. School of Mathematics and Statistics, Lingnan Normal University, Guangdong, China;3. Department of Mathematics, University of Macau, Macau SAR, China;4. UMacau Research Institute, Zhuhai, China |
| Abstract: | In this article, we show that the log empirical likelihood ratio statistic for the population mean converges in distribution to χ2(1) as n → ∞ when the population is in the domain of attraction of normal law but has infinite variance. The simulation results show that the empirical likelihood ratio method is applicable under the infinite second moment condition. |
| Keywords: | Confidence interval Domain of attraction of normal law Empirical likelihood Infinite variance |