Minimum distance estimators in extreme value distributions

Abstract

We define minimum distance estimators for the parameters of the extreme value distribution G_o based on the Cramer-von-Mises distance. These estimators are rather robust and consistent, but asymptotically less efficient than the maximum likelihood estimators which are not robust. A small simulation study for finite sample size show that under G_o the finite efficiency of the minimum distance estimators is rather similar to the maximum likelihood ones.

Keywords:

• Extreme value distribution
• Gumbel distribution
• minimum distance
• maximum likehood estimator
• censored samples
• efficiency
• robustness