Abstract
This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.)
1This research was performed while the author held an Adolph C. and Mary Sprague Miller Fellowship.
2 Now at Cornell University.
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References
Anscombe. F.J. (1960). Rejection of outliers. Technometrics 2 123–147.
Cramér, H. (1946). Mathematical Methods of Statistics. Princeton Univ. Press.
Hajek. J. (1962). Asymptotically most powerful rank order tests. Ann. Math. Statist. 33 1124–1147.
Hodges, J.L., Jr. and Lehmann. E. (1963). Estimates of location based on rank tests. Ann. Math. Statist. 34 598–611.
Hoeffding, W. (1948). A class of statistic» with asymptotically normal distributions. Ann. Math. Statist. 19 293–325.
LeCam, L. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. Univ. California Publ. Statist. 1 277–330.
LeCam, L. (1958). Les propriétés asymptotiques des solutions de Bayes. Publications de l’Institut de Statistique de l’Université de Paris. 7 17–35.
Loève, M. (1960). Probability Theory, (2nd ed.). Van Nostrand, New York.
Stein, C. (1956). Efficient nonparametric testing and estimation. Proc. Third Berkele Symp. Math. Statist, and Prob. (J. Neyman and L. LeCam, eds.) I 187–195.
Tukey, J.W. (1960). A survey of sampling from contaminated distributions. In Contributions to Probability and Statistics (ed. I. Olkin et al.). Stanford Univ. Press.
Wald. A. (1949) Note on the consistency of the M.L. estimate. Ann. Math. Statist. 20 595–601.
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© 1992 Springer-Verlag New York, Inc.
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Huber, P.J. (1992). Robust Estimation of a Location Parameter. In: Kotz, S., Johnson, N.L. (eds) Breakthroughs in Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4380-9_35
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DOI: https://doi.org/10.1007/978-1-4612-4380-9_35
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