In this paper we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for tail copulas or tail dependence functions for bivariate extremes. By applying the standard empirical likelihood method for a mean to the smoothed jackknife sample, the empirical likelihood ratio statistic can be calculated by simply solving a single equation. Therefore, this procedure is easy to implement. The Wilks' theorem for the empirical likelihood ratio statistic is proved, and a simulation study prefers the proposed method to the bootstrap method.
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Acknowledgements We thank three reviewers for their helpful comments. Peng’s research was supported by NSA grant H98230-10-1-0170 and Qi’s research was supported by NSA grant H98230-10-1-0161.
Copyright 2010 Elsevier B.V., All rights reserved.
- Confidence interval
- Empirical likelihood
- Tail copula