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

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Summary

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. 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 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.

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