M–Estimtors and l–estimators of location: uniform integrability and asymptotic risk–efficient sequential versions
- 1 January 1982
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Part C: Sequential Analysis
- Vol. 1 (1) , 27-56
- https://doi.org/10.1080/07474948208836003
Abstract
In the context of asymptotically minimum risk (sequential) point estimation of location of a symmetric distribution, M-and L-estimators are considered, and various properties of their sequential versions are studied. Asymptotic distributions of he allied stopping times are also derived. In this study, uniform integrability and moment convergence of (non-sequential) M- and L-estimators are established. These results have interest of therir own and provide the main tools for the proof of the other results presented. For the sequential estimators, their asymptotic risk efficiencies are shown to coincide with the asymptotic efficiencies of the respective non-sequential estimators; this enables one to construct the asymptotically minimax sequential M- and L-estimators in the model of contaminancy. Parallel results also hold for the rank estimators of location.Keywords
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