Limiting behaviour of a geometric-type estimator for tail indices

We propose a consistent estimator for the exponential tail coefficient of a d.f., that is directly related to least squares estimators of Schultze and Steinebach [Statist. Decis. 14 (1996) 353]. We investigate here the weak asymptotic properties of this geometric-type estimator, showing in particular that, under general conditions, its distribution is asymptotically normal. The results are then applied to the related problem of estimating the adjustment coefficient in risk theory [Insur.: Math. Econ. 10 (1991) 37]. A simulation study is performed in order to illustrate the finite sample behaviour of the proposed estimator.