M - Estimators and L - Estimators of Location ; Uniform Integrability and Asymptotic Risk - Efficient Sequential Versions

Sequential Mand L-estimators of location minimizing the risk asymptotically as the cost of one observation tends to 0 are constructed. Their asymptotic risk efficiencies are shown to coincide with the asymptotic efficiencies of the respective non-sequential estimators; this enables to construct the asymptotically minimax sequential Mand L-estimators in the model of contaminacy. The asymptotic distributions of the stopping times are derived for both types of estimators. The theorems on uniform integrability and moment convergence of (non-sequential) Mand L-estimators, developed as the main tools for the proofs, have an interest of their own. AMS 1970 Subject Classifications: Primary 62L12; Secondary 60F25