On consistent M -estimators: Tuning constants, unimodality and breakdown

Ivan Mizera

Kybernetika (1994)

  • Volume: 30, Issue: 3, page 289-300
  • ISSN: 0023-5954

How to cite

top

Mizera, Ivan. "On consistent $M$-estimators: Tuning constants, unimodality and breakdown." Kybernetika 30.3 (1994): 289-300. <http://eudml.org/doc/28317>.

@article{Mizera1994,
author = {Mizera, Ivan},
journal = {Kybernetika},
keywords = {big tuning constant conjecture; existence; uniqueness; location M- functionals; symmetric; asymmetric case; unimodality},
language = {eng},
number = {3},
pages = {289-300},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On consistent $M$-estimators: Tuning constants, unimodality and breakdown},
url = {http://eudml.org/doc/28317},
volume = {30},
year = {1994},
}

TY - JOUR
AU - Mizera, Ivan
TI - On consistent $M$-estimators: Tuning constants, unimodality and breakdown
JO - Kybernetika
PY - 1994
PB - Institute of Information Theory and Automation AS CR
VL - 30
IS - 3
SP - 289
EP - 300
LA - eng
KW - big tuning constant conjecture; existence; uniqueness; location M- functionals; symmetric; asymmetric case; unimodality
UR - http://eudml.org/doc/28317
ER -

References

top
  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. (1972) MR0331595
  2. P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968. (1968) Zbl0172.21201MR0233396
  3. B. R. Clarke, Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations, Ann. Statist. 11 (1983), 1196-1205. (1983) Zbl0541.62023MR0720264
  4. L. Davies, The asymptotics of S-estimators in the linear regression model, Ann. Statist. 18 (1990), 1651-1675. (1990) Zbl0719.62042MR1074428
  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. (1982) 
  6. D. A. Freedman, P. Diaconis, On Inconsistent M-estimates, Technical Report No. 170, Department of Statistics, Stanford University 1981. (1981) 
  7. D. A. Freedman, P. Diaconis, On inconsistent M-estimators, Ann. Statist. 10 (1982), 454-461. (1982) Zbl0496.62034MR0653520
  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 MR0829458
  9. D. C. Hoaglin F. Mosteller, J. W. Tukey, Understanding Robust and Exploratory Data Analysis, Wiley, New York 1983. (1983) MR1800901
  10. P. J. Huber, Robust estimators of a location parameter, Ann. Math. Statist. 35 (1964), 73-101. (1964) MR0161415
  11. P. J. Huber, Robust Statistics, Wiley, New York 1981. (1981) Zbl0536.62025MR0606374
  12. P. J. Huber, Finite sample breakdown of M- and P-estimators, Ann. Statist. 12 (1984), 119-126. (1984) Zbl0557.62034MR0733503
  13. I. A. Ibragimov, O kompozicii odnoveršinnych raspredelenij, Teor. Veroyatnost. i Primenen. 1 (1956), 283-288. (In Russian.) (1956) 
  14. S. Karlin, Total Positivity, Stanford University Press, Stanford 1968. (1968) Zbl0219.47030MR0230102
  15. I. Mizera, Weak continuity and identifiability of M-functionals, Thesis. Charles University, Prague 1993. (In Slovak.) (1993) 
  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. (1951) MR0047732

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.