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Empirical likelihood based confidence intervals for the tail index when γ<−1/2

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  • Sun, Haoze
  • Jiang, Yuexiang

Abstract

Empirical mortality data reveals that there is a finite age limit in the life span of humans, which means that it has a negative tail index. So far, there is a little literature on the confidence intervals for the tail index, especially for the negative tail index. In this paper, we construct its empirical likelihood based confidence intervals when γ<−1/2, which is known as the irregular case and derive the asymptotic χ2(1) distribution. At last a limited simulation study is conducted, which indicates that our method is better than the normal approximation in the sense of coverage probability and less sensitive to the selection of k.

Suggested Citation

  • Sun, Haoze & Jiang, Yuexiang, 2014. "Empirical likelihood based confidence intervals for the tail index when γ<−1/2," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 149-157.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:149-157
    DOI: 10.1016/j.spl.2013.10.001
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    References listed on IDEAS

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    1. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
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    3. Ngai Chan & Liang Peng & Rongmao Zhang, 2012. "Interval estimation of the tail index of a GARCH(1,1) model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 546-565, September.
    4. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    5. Deyuan Li & Liang Peng & Yongcheng Qi, 2011. "Empirical likelihood confidence intervals for the endpoint of a distribution function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 353-366, August.
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    Cited by:

    1. Ma, Yaolan & Jiang, Yuexiang & Huang, Wei, 2018. "Empirical likelihood based inference for conditional Pareto-type tail index," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 114-121.

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