Methods for estimating the upcrossings index: improvements and comparison

@article{Martins2015MethodsFE,
  title={Methods for estimating the upcrossings index: improvements and comparison},
  author={Ana Paula Martins and Jo{\~a}o Renato Sebasti{\~a}o},
  journal={Statistical Papers},
  year={2015},
  volume={60},
  pages={1317-1347}
}
The upcrossings index $$0\le \eta \le 1,$$0≤η≤1, as a measure of the degree of local dependence in the upcrossings of a high level by a stationary process, plays, together with the extremal index $$\theta ,$$θ, an important role in extreme events modelling. For stationary processes, verifying a long range dependence condition, upcrossings of high thresholds in different blocks can be assumed asymptotically independent and therefore blocks estimators for the upcrossings index can be easily… 
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