A NEW CALIBRATION METHOD OF CONSTRUCTING EMPIRICAL LIKELIHOOD-BASED CONFIDENCE INTERVALS FOR THE TAIL INDEX

Empirical likelihood has attracted much attention in the literature as a nonparametric method. A recent paper by Lu & Peng (2002) [Likelihood based confidence intervals for the tail index. Extremes 5, 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 χ² approximation has a serious undercoverage problem. Motivated by Tsao (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.