A new calibration method of constructing empirical likelihood-based confidence intervals for the tail index

Summary Empirical likelihood has attracted much attention in the literature as a nonparametric method. A recent paper by b9Lu & Peng (2002) [Likelihood based confidence intervals for the tail index. Extremes5, 337-352] applied this method to construct a confidence interval for the tail index of a heavy-tailed distribution. It turns out that the empirical likelihood method, as well as other likelihood-based methods, performs better than the normal approximation method in terms of coverage probability. However, when the sample size is small, the confidence interval computed using the χ ² approximation has a serious undercoverage problem. Motivated by b16Tsao (2004) [A new method of calibration for the empirical loglikelihood ratio. Statist. Probab. Lett.68, 305-314], this paper proposes a new method of calibration, which corrects the undercoverage problem.