  The extreme value dependence of regularly varying stationary time series can
be described by the spectral tail process. Drees, Segers and Warchol [Extremes
18(3): 369--402, 2015] proposed estimators of the marginal distributions of
this process based on exceedances over high deterministic thresholds and
analyzed their asymptotic behavior. In practice, however, versions of the
estimators are applied which use exceedances over random thresholds like
intermediate order statistics. We prove that these modified estimators have the
same limit distributions. This finding is corroborated in a simulation study,
but the version using order statistics performs a bit better for finite
samples.
