Summary
The infinitesimal robustness of the asymptotic variance of location M-estimators is investigated by means of the change-of-variance curve (CVC), which bears some resemblance to the influence curve (IC). It is proved that this CVC leads to a more stringent robustness property than the IC and that the Huber estimators are still optimal in this new sense.
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Collins, J.R.: Upper bounds on asymptotic variances of M-estimators of location. Ann. Statist. 5, 646–657 (1977)
Hampel, F.R.: Contributions to the theory of robust estimation. Unpublished dissertation, Berkeley: University of California 1968
Hampel, F.R.: Robust estimation: a condensed partial survey. Z. Wahrscheinlichkeitstheorie verw. Gebiete 27, 87–104 (1973)
Hampel, F.R.: The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69, 383–393 (1974)
Huber, P.J.: Robust estimation of a location parameter. Ann. Math. Statist. 35, 73–101 (1964)
Huber, P.J.: The behaviour of maximum likelihood estimates under nonstandard conditions. Proc. Fifth Berkeley Sympos. Math. Statist. Probab. 1, 221–233 Univ. Calif. (1967)
Wegman, E.J., Carroll, R.J.: A Monte Carlo study of robust estimators of location. Commun. Statist. (Theory and Methods) A6, 795–812 (1977)
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Rousseeuw, P.J. A new infinitesimal approach to robust estimation. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 127–132 (1981). https://doi.org/10.1007/BF00531978
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DOI: https://doi.org/10.1007/BF00531978