A remark on robustness and weak continuity of M-estimators

Brenton R. Clarke
2000 Journal of the Australian Mathematical Society  
Global weak continuity of M-functionals in a neighbourhood of the parametric distribution is established. This has implications for robustness of M-estimators vis a vis definitions put forward by Hampel. For instance the Tukey bisquare location estimator is robust on neighbourhoods of the parametric model, but the median is not. 2000 Mathematics subject classification: primary 62G35; secondary 62E20.
doi:10.1017/s144678870000149x fatcat:r6xty7rsczdfzjmgalsx73shme