Estimators Asymptotically Minimax in Wide Sense

✍ Scribed by Dr. Igor Vajda

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 322 KB
• Volume: 31
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710310706

✦ Synopsis

&timators of location are considered. HUBEB (1964) introduced estimators aymptotically minimax on the set 8 of all regular M-estimators, for a given contamination E and for the set Q of all regular symmetric alternative data sources. We extend hie concept by admitting arbitrary eeb 8 of regular M-eatimatora and arbitrary sets Q or regular symmetric alternative BourcBB, and a h by replacing the singletons { E } c (0.1) by arbitrary subsets 8 C (0.1). The resulting eetimator cannot in general be evaluated explicitly. But for finite T i t eliata and, if 8 and Q are finite too, it may be chosen by a computer. This extra burden is justified i n some c a s a since more than 100 yo relative efficiency gain against all Huber's HE is achievable in thie manner. Such gains are achieved for a nontrivial family Q by the estimator proposed in VAJDA (1984). with redescending influence curve, which is shown to be asymptotically minimax in wide sense.