Domains of weak continuity of statistical functionals with a view toward robust statistics

Volker Krätschmer, Alexander Schied and Henryk Zähle

Journal of Multivariate Analysis, 2017, vol. 158, issue C, 1-19

Abstract: 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 robustness property (Krätschmer et al. (2012, 2014)) or a local robustness property (Zähle (2016)) 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.

Keywords: (ψk)-weak topology; w-set; Qualitative robustness; Hampel’s theorem; Maximum likelihood estimator; Law-invariant convex risk measure; Aggregation robustness; Orlicz space (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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DOI: 10.1016/j.jmva.2017.02.005

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