  In this work, we deal with extreme value theory in the context of continued
fractions using techniques from probability theory, ergodic theory and real
analysis. We give an upper bound for the rate of convergence in the
Doeblin-Iosifescu asymptotics for the exceedances of digits obtained from the
regular continued fraction expansion of a number chosen randomly from $(0,1)$
according to the Gauss measure. As a consequence, we significantly improve the
best known upper bound on the rate of convergence of the maxima in this case.
We observe that the asymptotics of order statistics and the extremal point
process can also be investigated using our methods.
