A0570
Title: Asymptotic properties of the maximum likelihood estimator within the block maxima framework
Authors: David Carl - Bocconi University (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Stefano Rizzelli - University of Padova (Italy)
Abstract: The asymptotic properties of the maximum likelihood estimator for the extreme value index within the block maxima setting are still not fully understood. So far, it has been shown that likelihood maximizers over compact sets that contain the truth are consistent, but no convergence rates for such estimators were derived. On the other hand, for suitably fast shrinking sets around the truth, there exist local maximizers of the likelihood that are asymptotically Gaussian distributed with the usual parametric convergence rate and that are eventually unique. In this work, we show that we can extend the results concerning uniqueness, convergence rate, and asymptotic Gaussianity to likelihood maximizers over compact sets if the extreme value index is positive.
