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Pires, Juliana F.; Cysneiros, Audrey H. M. A.; Cribari-Neto, Francisco

Improved inference for the generalized Pareto distribution. (English) Zbl 1404.62020

Braz. J. Probab. Stat. 32, No. 1, 69-85 (2018).
Summary: The generalized Pareto distribution is commonly used to model exceedances over a threshold. In this paper, we obtain adjustments to the generalized Pareto profile likelihood function using the likelihood function modifications proposed by O. Barndorff-Nielsen [Biometrika 70, 343–365 (1983; Zbl 0532.62006)], D. R. Cox and N. Reid [J. R. Stat. Soc., Ser. B 55, No. 2, 467–471 (1993; Zbl 0797.62015)], D. A. S. Fraser and N. Reid [Util. Math. 47, 33–53 (1995; Zbl 0829.62006); with J. Wu, Biometrika 86, No. 2, 249–264 (1999; Zbl 0932.62003)], and T. A. Severini [ibid. 86, No. 2, 235–247 (1999; Zbl 0943.62016)]. We consider inference on the generalized Pareto distribution shape parameter, the scale parameter being a nuisance parameter. Bootstrap-based testing inference is also considered. Monte Carlo simulation results on the finite sample performances of the usual profile maximum likelihood estimator and profile likelihood ratio test and also their modified versions is presented and discussed. The numerical evidence favors the modified profile maximum likelihood estimators and tests we propose. Finally, we consider two real datasets as illustrations.

Cited in 1 Document

MSC:

62E15 Exact distribution theory in statistics
62F10 Point estimation
62F03 Parametric hypothesis testing
60E05 Probability distributions: general theory
62P12 Applications of statistics to environmental and related topics

Keywords:

bootstrap; generalized Pareto distribution; likelihood ratio test; maximum likelihood estimation; profile likelihood

Citations:

Zbl 0532.62006; Zbl 0797.62015; Zbl 0829.62006; Zbl 0932.62003; Zbl 0943.62016

Software:

ismev; Ox
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\textit{J. F. Pires} et al., Braz. J. Probab. Stat. 32, No. 1, 69--85 (2018; Zbl 1404.62020)
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