Kybernetika 30 no. 3, 289-300, 1994

On consistent M-estimators: Tuning constants, unimodality and breakdown

Ivan Mizera


The existence and uniqueness of values of location M-functional are explored. For the symmetric population distributions, the role of studentization is revealed - the Freedman-Diaconis conjecture is proved. The asymmetric case is studied with respect to unimodality considerations. The lower bound for the breakdown of studentized estimators is derived.


62E10, 62F35, 62F10