Advertisement

Robust Estimation in the Logistic Regression Model

  • Ana M. Bianco
  • Víctor J. Yohai
Part of the Lecture Notes in Statistics book series (LNS, volume 109)

Abstract

A new class of robust and Fisher-consistent M-estimates for the logistic regression models is introduced. We show that these estimates are consistent and asymptotically normal. Their robustness is studied through the computation of asymptotic bias curves under point-mass contamination for the case when the covariates follow a multivariate normal distribution. We illustrate the behavior of these estimates with two data sets. Finally, we mention some possible extensions of these M-estimates for a multinomial response.

Key words and phrases

logistic regression model M-estimates robust estimates 

AMS 1991 subject classifications

Primary 62F35, 62J12 secondary 62F12 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Carroll, R.J. and Pederson, S. (1993): On robustness in the logistic regression model. Biometrika 55 693–706.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Cook, R.D. and Weisberg, S. (1982): Residuals and Influence in Regression. Chapman & Hall, London.zbMATHGoogle Scholar
  3. [3]
    Copas, J.B. (1988): Binary regression models for contaminated data. J. Roy. Statist. Soc. B 50 225–265.MathSciNetGoogle Scholar
  4. [4]
    Hampel, F.R. (1971): A general definition of qualitative robustness. Ann. Math. Statist. 42 1887–1896.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Huber, P.J. (1967): The behavior of maximum likelihood estimates under non-standard conditions. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 1 221–233. Univ. of California Press, Berkeley.Google Scholar
  6. [6]
    Johnson, W. (1985): Influence measures for logistic regression: another point of view. Biometrika 72 59–66.CrossRefGoogle Scholar
  7. [7]
    Künsch, H.R., Stefanski, L.A. and Carroll, R.J. (1989): Conditionally unbiased bounded influence estimation in general regression models, with applications to generalized linear models. J. Amer. Statist. Assoc. 84 460–466.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Martin, R.D., Yohai, V.J. and Zamar, R.H. (1989): Min-max bias robust regression. Ann. Statist. 17 1608–1630.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Neider, J.A. and Mead, R. (1965): Computer Journal 7 308.Google Scholar
  10. [10]
    Pregibon, D. (1981): Logistic regression diagnostics. Ann. Statist. 9 705–724.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    Pregibon, D. (1982): Resistent fits for some commonly used logistic models with medical applications. Biometrics 38 485–498.CrossRefGoogle Scholar
  12. [12]
    Stefanski, L.A., Carroll, R.J. and Ruppert D. (1986): Optimally bounded score functions for generalized linear models with applications to logistic regression. Biometrika 73 413–425.MathSciNetzbMATHGoogle Scholar
  13. [13]
    Yohai, V.J. (1987): High breakdown point and high efficiency robust estimates for regression. Ann. Statist. 15 692–656.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Ana M. Bianco
    • 1
  • Víctor J. Yohai
    • 2
    • 3
  1. 1.Universidad de Buenos AiresArgentina
  2. 2.Universidad de San AndrésArgentina
  3. 3.Universidad de Buenos AiresArgentina

Personalised recommendations