Diagnostics of Regression Model: Test of Goodness of Fit

  • Asunción Maria Rubio
  • Jan Ámos Víšek
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

A test statistic for goodness of fit of the M-estimates of the linear regression model is proposed and its asymptotic behaviour is described. Numerical study on real data is included.

Key words

Diagnostic of residuals weighted Hellinger distance asymptotic normality numerical study 

AMS classification

62J05 62J15 

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References

  1. Csőrgő, M., Révész, P. (1981): Strong Approximations in Probability and Statistics. Budapest: Akadémiai Kiadó.Google Scholar
  2. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A. (1986): Robust Statistics-The Approach Based on Influence Functions. Wiley, New York.MATHGoogle Scholar
  3. Hettmansperger, T. P., Sheater, S.J. (1992): A cautionary note on the method of least median of squares. The American Statistician, May 1993, 46, pp 79–83.MathSciNetGoogle Scholar
  4. Hewitt, E., Stromberg, K. (1965): Real and Abstract Analysis. Berlin: Springer-Verlag.MATHCrossRefGoogle Scholar
  5. Huber, P. J. (1973): Robust regression: Asymptotics, conjectures and Monte Carlo. Ann. Statist. 1, 799–821.MathSciNetMATHCrossRefGoogle Scholar
  6. Jurecková, J. (1988): Constistency of M-estimators of vector parameters. Proc. of the Fourth Prague Symposium on Asymptotic Statistics, Charles University, Prague, 305–312.Google Scholar
  7. Mason, R. L., Gunst, R. F. and Hess, J. L. (1989): Statistical Design and Analysis of Experiments. New York: John Wiley.Google Scholar
  8. Rousseeuw, P.J., Leroy, A.M. (1987): Robust Regression and Outlier Detection. New York: J.Wiley & Sons.MATHCrossRefGoogle Scholar
  9. Visek, J. A. (1985): Estimating contamination level. Proc. of the 5th Pannonian Symposium on Mathematical Statistics, Visegrád, Hungary, 401-414.Google Scholar
  10. Visek, J. A. (1992a): Adaptive maximum-likelihood-like estimation in linear models. Kybernetika 28, 357–382 and 454-471.MathSciNetMATHGoogle Scholar
  11. Visek, J. A. (1992b): Stability of regression model estimates with respect to sub-samples. Computational Statistics 7, 183–203.MathSciNetMATHGoogle Scholar
  12. Víšek, J. A. (1992c): Problems connected with selection of robust procedure. Proc. of PR0BASTAT’91, Printing House of the Technical University of Liptovsky Mikuláš, eds. A. Pázrnan and J. Volaufová, 189-203.Google Scholar
  13. Visek, J. A. (1993): A cautionary note on the method of Least Median of Squares reconsidered. Submitted to The American Statistician.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Asunción Maria Rubio
    • 1
  • Jan Ámos Víšek
    • 2
  1. 1.Departamento de Matemáticas, Facultad de VeterinariaUniversidad de ExtremaduraCáceresSpain
  2. 2.Department of Stochastic Informatics, Institute of Information Theory and AutomationAcademy of Sciences the Czech republicCzech Republic

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