A location-invariant non-positive moment-type estimator of the extreme value index

ABSTRACT

This paper investigates a class of location invariant non-positive moment-type estimators of extreme value index, which is highly flexible due to the tuning parameter involved. Its asymptotic expansions and its optimal sample fraction in terms of minimal asymptotic mean square error are derived. A small scale Monte Carlo simulation turns out that the new estimators, with a suitable choice of the tuning parameter driven by the data itself, perform well compared to the known ones. Finally, the proposed estimators with a bootstrap optimal sample fraction are applied to an environmental data set.

KEYWORDS:

• Bootstrap methodology
• Extreme value index
• Extreme value statistics
• Location-invariant moment-type estimation.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60G70
• Secondary 65C05.

Acknowledgments

The authors would like to thank Zuoxiang Peng and Enkelejd Hashorva for useful discussions.

Additional information

Funding

The authors would like to thank the referees for their important suggestions which significantly improved this contribution. C. Liu and C. Ling acknowledge the National Natural Science Foundation of China grant (11604375) and the Natural Science Foundation Project of CQ (cstc2016jcyjA0036). C. Ling is also supported by the China Postdoctoral Science Foundation (2016M602624) and Chinese Government Scholarship (201708505031).