Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domains of weak continuity of statistical functionals with a view toward
  robust statistics   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 classical sense. However, these estimators may
nevertheless satisfy a weak (Kr\"atschmer/Schied/Z\"ahle 2012, 2014) or a local
(Z\"ahle 2016) robustness property on relevant sets of distributions. One aim
of our paper is to identify sets of local robustness, and to explain the
benefit of the knowledge of such sets. For instance, we will be able to
demonstrate that many maximum likelihood estimators are robust on their natural
parametric domains. A second aim consists in extending the general theory of
robust estimation to our local framework. In particular we provide a
corresponding Hampel-type theorem linking local robustness of a plug-in
estimator with a certain continuity condition.

17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th