In this paper, we build a two-step estimator γSTEP, which satisfies √k(γSTEP - γML) →P 0, where γML is the well-known maximum likelihood estimator of the extreme value index. Since the two-step estimator γSTEP can be calculated easily as a function of the observations, it is much simpler to use in practice. By properly choosing the first step estimator, such as the Pickands estimator, we can even get a shift and scale invariant estimator with the above property.

Additional Metadata
Keywords Extreme value index, Maximum likelihood, Shift and scale invariant estimator
Persistent URL dx.doi.org/10.1007/s10687-008-0058-2, hdl.handle.net/1765/76694
Journal Extremes: statistical theory and applications in science, engineering and economics
Citation
Zhou, C. (2008). A two-step estimator of the extreme value index. Extremes: statistical theory and applications in science, engineering and economics, 11(3), 281–302. doi:10.1007/s10687-008-0058-2