Skip to main content

Bias- and efficiency-robustness of general M-estimators for regression with random carriers

Part of the Lecture Notes in Mathematics book series (LNM,volume 757)

Keywords

  • Asymptotic Normality
  • Asymptotic Variance
  • Influence Function
  • Robust Regression
  • Breakdown Point

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Beaton, A.E. and Tukey, J.W. (1974). The fitting of power series, meaning polynomials, illustrated on bandspectroscopic data. Technometrics 16, 147–185.

    CrossRef  MATH  Google Scholar 

  • Daniel, C. and Wood, F.S. (1971). Fitting equations to data. Wiley, New York.

    MATH  Google Scholar 

  • Denby, L. and Larsen, (1977). Robust regression estimators compared via Monte Carlo. Comm. Stat. A6 (4), 335–362.

    CrossRef  MATH  Google Scholar 

  • Hampel, F.R. (1971). A general qualitative definition of robustness. Ann. Math. Statist. 42, 1887–1896.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Hampel, F.R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69, 383–394.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Hampel, F.R. (1977). Modern trends in the theory of robustness. Research report No. 13. Fachgruppe für Statistik-ETH Zürich.

    Google Scholar 

  • Hampel, F.R. (1978). Optimally bounding the gross-error-sensitivity and the influence of position in factor space. Research report No. 18. Fachgruppe für Statistik-ETH Zürich.

    Google Scholar 

  • Hill, R.W. (1977). Robust regression when there are outliers in the carriers. Ph.D.Thesis, Statistics Department, Harvard University.

    Google Scholar 

  • Holland, P.W. (1973). Monte Carlo for robust regression: the swindle unmasked. Working paper No. 10. National Bureau of Economic Research, Inc.

    Google Scholar 

  • Huber, P.J. (1964). Robust estimation of a location paprameter. Ann. Math. Statist. 35, 73–101.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Huber, P.J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proc. Fifth Berkeley Symp. Prob. 1, 221–233. University of California Press.

    MathSciNet  MATH  Google Scholar 

  • Huber, P.J. (1973). Robust regression: Asymptotic, conjectures, and Monte Carlo. Ann. Statist. 1, 799–821.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Huber, P.J. (1977). Robust covariances. In: Statistical Decision Theory and Related Topics II, 165–191. Academic Press, New York.

    CrossRef  Google Scholar 

  • Krasker, W.S. (1978). Estimation in linear regression models with disparate data points. Unpublished manuscript.

    Google Scholar 

  • Mallows, C. (1975). On some topics in robustness. Unpublished memorandum, Bell Telephone Laboratory, Murray Hill.

    Google Scholar 

  • Maronna, R.A. (1976) Robust M-estimators of multivariate location and scatter. Ann. Statist. 4, 51–67.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Maronna, R.A. and Yohai, V.J. (1978). Asymptotic behavior of general M-estimators for regression and scale with random carriers. Submitted for publication.

    Google Scholar 

  • Yohai, V.J. and Klein, R. (1978). Asymptotic behavior of iterative M-estimators. Unpublished manuscript.

    Google Scholar 

  • Yohai, V.J. and Maronna, R.A. (1976). Location estimators based on linear combinations of modified order statistics. Comm. Stat. A5, 481–486.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

Maronna, R., Bustos, O., Yohai, V. (1979). Bias- and efficiency-robustness of general M-estimators for regression with random carriers. In: Gasser, T., Rosenblatt, M. (eds) Smoothing Techniques for Curve Estimation. Lecture Notes in Mathematics, vol 757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098492

Download citation

  • DOI: https://doi.org/10.1007/BFb0098492

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09706-8

  • Online ISBN: 978-3-540-38475-5

  • eBook Packages: Springer Book Archive