Abstract. We study the asymptotic behavior of large deviation probabilities for a general class of tail index estimators. This new class consists of the generalized version of the weighted least-squares estimators proposed by Viharos [9] and also contains the class of kernel estimators obtained by Csörgő et al. [3]. Based on the large deviation probabilities, a comparison of the members of this class can be made. The Hill estimator turns out to have optimal rate of convergence within a subclass of estimators.

AMS Subject Classification (1991): 62G32, 60F10

Received August 14, 2007, and in revised form November 20, 2007. (Registered under 6023/2009.)