Estimating the parameters of rare events

In this paper the estimation of certain parameters of the extreme order statistics of stationary observations is considered in a general framework. These parameters are resulted from dependence, and hence their inference is substantially different from similar considerations in the i.i.d. context. Variants of estimators that are functionals of the empirical 'cluster size' distribution are proposed, and such properties as consistency and asymptotic normality are studied. Special emphasis is given to estimating the extremal index.