Skip to main content
SpringerLink
Log in

Strong consistency of M-estimates in linear models

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

The strong consistency of M-estimates of the regression coefficients in a linear model under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment condition. Especially, in some important circumstances, onlyE|ψ(ek)|q for some q > 1 is needed, where ψ{ek} is some score function of random error.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Huber, P. J., Robust regression, Ann. Statist., 1973, 1: 799–821.

    Article  MathSciNet  MATH  Google Scholar 

  2. Huber, P. J., Robust Statistics, New York: John Wiley, 1981.

    MATH  Google Scholar 

  3. Bai, Z. D., Rao, C. R, Wu, Y., M-estimation of multivariate linear regression parameters under a convex discrepancy function, Statistica Sinica, 1992, 2:237–254.

    MathSciNet  MATH  Google Scholar 

  4. Rao, C. R., Toutenburg, H., Linear Models, Least Squares and Alternatives, New York: Springer-Verlag, 1995.

    MATH  Google Scholar 

  5. Chen, X. R., Zhao, L. C., M-Methods in Linear Model, Shanghai: Shanghai Scientific & Technical Publishers (in Chinese), 1996.

    Google Scholar 

  6. Jurečková, J., Sen, P. K., Robust Statistical Procedures: Asymptotics and Interrelations, New York: Wiley, 1996.

    MATH  Google Scholar 

  7. Zhao Lincheng, Some contributions to M-estimation in linear models, J. Statist. Plann. Inference, 2000, 88: 189–203.

    Article  MathSciNet  MATH  Google Scholar 

  8. Yohai, V. J., Maronna, R. A., Asymptotic behavior of M-estimators for the linear model, Ann. Statist., 1979,7: 258–268.

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhao, L. C., Rao, C. R., Chen, X. R., A note on the consistency of M-estimates in linear models, in Stochastic Process, A Festschrift in Honour of Gopinath Kallianpur (eds. Cambanis, S., Ghosh, J. K., Karandikar, R. L. et al.), New York: Springer-Verlag, 1993, 359–367.

    Google Scholar 

  10. Rao, C. R., Zhao, L. C., On the consistency of M-estimate in a linear model obtained through an estimating equation, Statist. Probab. Letters, 1992,14: 79–84.

    Article  MathSciNet  MATH  Google Scholar 

  11. Wu, Y. H., Strong consistency and exponential rate of the“minimum L1-norm”estimates in linear regression models, Computational Statistics and Data Analysis, 1988,6:285–295.

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, X. R., Bai, Z. D., Zhao, L. C. et al., Consistency of minimum L1-norm estimates in linear models, in The Development of Statistics: Recent Contributions from China (eds. Chen, X. R., Fang, K. T., Yang, C. C.), Pitman Research Notes in Mathematics, Series 258, Harlow: Longman Scientific & Technical, 1992.

    Google Scholar 

  13. Chen, X. R., Zhao, L. C., Strong consistency of M-estimates of multiple regression coefficients, Systems Science and Mathematical Sciences, 1995, 8: 82–87.

    MathSciNet  MATH  Google Scholar 

  14. Yang Shanchao, Strong consistency of M estimator in linear model, Acta Math. Sinica (in Chinese), 2002, 45(1): 21–28.

    MATH  Google Scholar 

  15. Bannett, G., Probability inequalities for sums of independent random variables, J. Amer. Statist. Assoc., 1962, 57(1): 33- 45.

    Article  Google Scholar 

  16. Zhao, L. C., Rates of a.s. convergence of the estimation of error variance in linear models, Chin. Ann. of Math., Ser. B, 1983,4(1): 95–103.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Finance, University of Science and Technology of China, 230026, Hefei, China

    Zhao Lincheng

Authors
  1. Zhao Lincheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhao Lincheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lincheng, Z. Strong consistency of M-estimates in linear models. Sci. China Ser. A-Math. 45, 1420–1427 (2002). https://doi.org/10.1007/BF02880036

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02880036

Keywords

Search

Navigation