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On consistent $M$-estimators: Tuning constants, unimodality and breakdown
Kybernetika, Tome 30 (1994) no. 3, pp. 289-300 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Classification : 62E10, 62F10, 62F35 
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     url = {http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a8/}
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Mizera, Ivan. On consistent $M$-estimators: Tuning constants, unimodality and breakdown. Kybernetika, Tome 30 (1994) no. 3, pp. 289-300. http://geodesic.mathdoc.fr/item/KYB_1994_30_3_a8/

[1] D. F. Andrews P. J. Bickel F. R. Hampel P. J. Huber W. H. Rogers, J. W. Tukey: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton 1972. | MR

[2] P. Billingsley: Convergence of Probability Measures. Wiley, New York 1968. | MR | Zbl

[3] B. R. Clarke: Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations. Ann. Statist. 11 (1983), 1196-1205. | MR | Zbl

[4] L. Davies: The asymptotics of S-estimators in the linear regression model. Ann. Statist. 18 (1990), 1651-1675. | MR | Zbl

[5] D. L. Donoho, P. J. Huber: The notion of breakdown point. In: Festschrift in Honor of Erich Lehmann (K. Doksum and J. L. Hodges, eds.), Wadsworth, Belmont, CA 1982.

[6] D. A. Freedman, P. Diaconis: On Inconsistent M-estimates. Technical Report No. 170, Department of Statistics, Stanford University 1981.

[7] D. A. Freedman, P. Diaconis: On inconsistent M-estimators. Ann. Statist. 10 (1982), 454-461. | MR | Zbl

[8] F. R. Hampel E. M. Ronchetti P. J. Rousseeuw, W. A. Stahel: Robust Statistics -- The Approach Based on Influence Functions. Wiley, New York 1986 | MR

[9] D. C. Hoaglin F. Mosteller, J. W. Tukey: Understanding Robust and Exploratory Data Analysis. Wiley, New York 1983. | MR

[10] P. J. Huber: Robust estimators of a location parameter. Ann. Math. Statist. 35 (1964), 73-101. | MR

[11] P. J. Huber: Robust Statistics. Wiley, New York 1981. | MR | Zbl

[12] P. J. Huber: Finite sample breakdown of M- and P-estimators. Ann. Statist. 12 (1984), 119-126. | MR | Zbl

[13] I. A. Ibragimov: O kompozicii odnoveršinnych raspredelenij. Teor. Veroyatnost. i Primenen. 1 (1956), 283-288. (In Russian.)

[14] S. Karlin: Total Positivity. Stanford University Press, Stanford 1968. | MR | Zbl

[15] I. Mizera: Weak continuity and identifiability of M-functionals. Thesis. Charles University, Prague 1993. (In Slovak.)

[16] I. J. Schoenberg: On Pólya frequency functions. Part I: The totally positive functions and their Laplace transforms. J. Analyse Math. 1 (1951), 331-374. | MR