Edgeworth expansion for an estimator of the adjustment coefficient

We establish an Edgeworth expansion for an estimator of the adjustment coefficient R, directly related to the geometric-type estimator for general exponential tail coefficients, proposed in [Brito, M., Freitas, A.C.M., 2003. Limiting behaviour of a geometric-type estimator for tail indices. Insurance Math. Econom. 33, 211-226].Using the first term of the expansion, we construct improved confidence bounds for R. The accuracy of the approximation is illustrated using an example from insurance (cf. [Schultze, J., Steinebach, J., 1996. On least squares estimates of an exponential tail coefficient. Statist. Dec. 14, 353-372]).