| Title:
|
On consistent $M$-estimators: Tuning constants, unimodality and breakdown (English) |
| Author:
|
Mizera, Ivan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
30 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
289-300 |
| . |
| Category:
|
math |
| . |
| MSC:
|
62E10 |
| MSC:
|
62F10 |
| MSC:
|
62F35 |
| idZBL:
|
Zbl 0815.62013 |
| idMR:
|
MR1291931 |
| . |
| Date available:
|
2009-09-24T18:47:40Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125162 |
| . |
| Reference:
|
[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 0331595 |
| Reference:
|
[2] P. Billingsley: Convergence of Probability Measures.Wiley, New York 1968. Zbl 0172.21201, MR 0233396 |
| Reference:
|
[3] B. R. Clarke: Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations.Ann. Statist. 11 (1983), 1196-1205. Zbl 0541.62023, MR 0720264 |
| Reference:
|
[4] L. Davies: The asymptotics of S-estimators in the linear regression model.Ann. Statist. 18 (1990), 1651-1675. Zbl 0719.62042, MR 1074428 |
| Reference:
|
[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. |
| Reference:
|
[6] D. A. Freedman, P. Diaconis: On Inconsistent M-estimates.Technical Report No. 170, Department of Statistics, Stanford University 1981. |
| Reference:
|
[7] D. A. Freedman, P. Diaconis: On inconsistent M-estimators.Ann. Statist. 10 (1982), 454-461. Zbl 0496.62034, MR 0653520 |
| Reference:
|
[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 0829458 |
| Reference:
|
[9] D. C. Hoaglin F. Mosteller, J. W. Tukey: Understanding Robust and Exploratory Data Analysis.Wiley, New York 1983. MR 1800901 |
| Reference:
|
[10] P. J. Huber: Robust estimators of a location parameter.Ann. Math. Statist. 35 (1964), 73-101. MR 0161415 |
| Reference:
|
[11] P. J. Huber: Robust Statistics.Wiley, New York 1981. Zbl 0536.62025, MR 0606374 |
| Reference:
|
[12] P. J. Huber: Finite sample breakdown of M- and P-estimators.Ann. Statist. 12 (1984), 119-126. Zbl 0557.62034, MR 0733503 |
| Reference:
|
[13] I. A. Ibragimov: O kompozicii odnoveršinnych raspredelenij.Teor. Veroyatnost. i Primenen. 1 (1956), 283-288. (In Russian.) |
| Reference:
|
[14] S. Karlin: Total Positivity.Stanford University Press, Stanford 1968. Zbl 0219.47030, MR 0230102 |
| Reference:
|
[15] I. Mizera: Weak continuity and identifiability of M-functionals.Thesis. Charles University, Prague 1993. (In Slovak.) |
| Reference:
|
[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 0047732 |
| . |
