Maximum penalized likelihood estimation for the endpoint and exponent of a distribution

@article{Wang2018MaximumPL,
  title={Maximum penalized likelihood estimation for the endpoint and exponent of a distribution},
  author={Fang Wang and Liang Peng and Yongcheng Qi and Meiping Xu},
  journal={Statistica Sinica},
  year={2018},
  volume={29},
  pages={203-224}
}
Consider a random sample from a regularly varying distribution function with a finite right endpoint θ and an exponent α of regular variation. The primary interest of the paper is to estimate both the endpoint and the exponent. Since the distribution is semiparametric and the endpoint and the exponent reveal asymptotic properties of the right tail for the distribution, inference can only be based on a few of the largest observations in the sample. The conventional maximum likelihood method can… 
Rejoinder of “On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures”
I am pleased that my review article has stimulated such broader and thoughtful discussions in probability theory, theoretical statistics, estimation methods, and applications. The discussants have
Maximum penalized likelihood estimation for the endpoint and exponent of a distribution
Consider a random sample from a regularly varying distribution function with a finite right endpoint θ and an exponent α of regular variation. The primary interest of the paper is to estimate both

References

SHOWING 1-7 OF 7 REFERENCES
A General Estimator for the Right Endpoint
In this paper, the right endpoint estimation problem is tackled via a recent estimator envisioned for distributions in the Gumbel domain, a domain of attraction induced by the extreme value theorem.
ESTIMATION OF THE FINITE RIGHT ENDPOINT IN THE GUMBEL DOMAIN
A simple estimator for the finite right endpoint of a distribution function in the Gumbel max-domain of attraction is proposed. Large sample properties such as consistency and the asymptotic
Extreme value theory : an introduction
This treatment of extreme value theory is unique in book literature in that it focuses on some beautiful theoretical results along with applications. All the main topics covering the heart of the
A moment estimator for the index of an extreme-value distribution
On generalise l'estimateur bien connu de Hill de l'indice d'une fonction de reparatition avec queue de variation reguliere a une estimation de l'indice d'une loi de valeurs extremes. On demontre la
On Estimating the Endpoint of a Distribution
Maximum penalized likelihood estimation for the endpoint and exponent of a distribution
Consider a random sample from a regularly varying distribution function with a finite right endpoint θ and an exponent α of regular variation. The primary interest of the paper is to estimate both
Probability Theory I, 4th Edition. Springer, New York. 26 Statistica Sinica: Newly accepted Paper (accepted version subject to English editing
  • 1977