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Efficient likelihood-based inference for the generalized Pareto distribution

Author

Listed:
  • Hideki Nagatsuka

    (Chuo University)

  • N. Balakrishnan

    (McMaster University)

Abstract

It is well known that inference for the generalized Pareto distribution (GPD) is a difficult problem since the GPD violates the classical regularity conditions in the maximum likelihood method. For parameter estimation, most existing methods perform satisfactorily only in the limited range of parameters. Furthermore, the interval estimation and hypothesis tests have not been studied well in the literature. In this article, we develop a novel framework for inference for the GPD, which works successfully for all values of shape parameter k. Specifically, we propose a new method of parameter estimation and derive some asymptotic properties. Based on the asymptotic properties, we then develop new confidence intervals and hypothesis tests for the GPD. The numerical results are provided to show that the proposed inferential procedures perform well for all choices of k.

Suggested Citation

  • Hideki Nagatsuka & N. Balakrishnan, 2021. "Efficient likelihood-based inference for the generalized Pareto distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1153-1185, December.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:6:d:10.1007_s10463-020-00782-z
    DOI: 10.1007/s10463-020-00782-z
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    References listed on IDEAS

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    1. Castillo, Joan del & Serra, Isabel, 2015. "Likelihood inference for generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 116-128.
    2. David E. Giles & Hui Feng & Ryan T. Godwin, 2016. "Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2465-2483, April.
    3. Song, Jongwoo & Song, Seongjoo, 2012. "A quantile estimation for massive data with generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 143-150, January.
    4. Iliopoulos, G. & Balakrishnan, N., 2009. "Conditional independence of blocked ordered data," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1008-1015, April.
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