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math.ST2021★ 1 cited
The roughness exponent and its model-free estimation
Xiyue Han, Alexander Schied
Motivated by pathwise stochastic calculus, we say that a continuous real-valued function admits the roughness exponent if the variation of converges to…
math.ST2015
Domains of weak continuity of statistical functionals with a view toward robust statistics
Volker Krätschmer, Alexander Schied, Henryk Zähle
Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the cl…
math.ST2014
Quasi-Hadamard differentiability of general risk functionals and its application
Volker Krätschmer, Alexander Schied, Henryk Zähle
We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differenti…