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The extreme value dependence of regularly varying stationary time series canbe described by the spectral tail process. Drees, Segers and Warchol [Extremes18(3): 369--402, 2015] proposed estimators of the marginal distributions ofthis process based on exceedances over high deterministic thresholds andanalyzed their asymptotic behavior. In practice, however, versions of theestimators are applied which use exceedances over random thresholds likeintermediate order statistics. We prove that these modified estimators have thesame limit distributions. This finding is corroborated in a simulation study,but the version using order statistics performs a bit better for finitesamples.

Peak-over-Threshold Estimators for Spectral Tail Processes: Random vs Deterministic Thresholds