Empirical likelihood ratio under infinite second moment
Conghua Cheng, Yiming Liu, Zhi Liu · Communication in Statistics- Theory and Methods · 2016
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.