Skip to main content
SpringerLink
Log in

Further study strong consistency of M estimator in linear model for \(\tilde \rho\)-mixing random samples

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The strong consistency of M estimators of the regression parameters in linear models for \(\tilde \rho\)-mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu (2005) is improved essentially on the moment conditions.

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.

Similar content being viewed by others

References

  1. P. J. Huber, Robust regression: Asymptotics, conjectures and Monte Carlo, Ann. Statist., 1973, 1(5): 799–821.

    Article  MathSciNet  MATH  Google Scholar 

  2. X. R. Chen and L. C. Zhao, Strong consistency of M-estimates of multiple regression coefficients, Systems Science and Mathematical Sciences, 1995, 8(1): 82–87.

    MathSciNet  MATH  Google Scholar 

  3. X. R. Chen and L. C. Zhao, M-Methods in Linear Model, Shanghai Scientific and Technical Publishers, Shanghai, 1996.

    Google Scholar 

  4. X. M. He and Q. M. Shao, A general bahadur representation of M estimator and its application to linear regression with nonstochastic designs, Ann. Statist., 1996, 24(6): 2608–2630.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. C. Yang, Strong consistency of M estimator in linear model, Acta Mathematica Sinica, Chinese Series, 2002, 45(1): 21–28.

    MathSciNet  MATH  Google Scholar 

  6. J. R. Collins and V. D. Szatmari, Maximal asymptotic siases of M estimators of location with preliminary scale estimates, Comm. Statist. Theory Methods, 2004, 33(8): 1877–1866.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Georgios, Application of M estimators to cross-section effect models, Comm. Statist. Simulation Computation, 2005, 34(3): 601–616.

    Article  MATH  Google Scholar 

  8. Q. Y. Wu, Strong consistency of M estimator in linear model for \(\tilde \rho\)-mixing samples, Acta Mathematica Scientia, 2005, 25A(1): 41–46.

    Google Scholar 

  9. Q. Y. Wu, Strong consistency of M estimator in linear model for negatively associated samples, Journal of Systems Science & Complexity, 2006, 19(4): 592–600.

    Article  MathSciNet  MATH  Google Scholar 

  10. C. Djalil and C. Didier, On the strong consistency of asymptoticM estimators, Journal of Statistical Planning and Inference, 2007, 137: 2774–2783.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Seija, T. Sara, and O. Hannu, Symmetrized M estimators of multivariate scatter, Journal of Multivariate Analysis, 2007, 98: 1611–1629.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. C. Bradley, On the spectral density and asymptotic normality of weakly dependent random fields, Theoret. Probab., 1992, 5: 355–373.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Bryc and W. Smolenski, Moment conditions for almost sure convergence of weakly correlated random variables, Proc. Amer.Math. Soc., 1993, 199(2): 629–635.

    Article  MathSciNet  Google Scholar 

  14. C. M. Goldie and P. E. Greenwood, Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes, Ann. Probab., 1986, 14(3): 817–839.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. C. Yang, Some moment inequalities for partial sums of random variables and their applications, Chinese Sci. Bull., 1998, 43(17): 1823–1827.

    Article  Google Scholar 

  16. Q. Y. Wu, Some convergence properties for \(\tilde \rho\)-mixing sequences, Engng. Math., 2001, 18(3): 58–64.

    MATH  Google Scholar 

  17. Q. Y. Wu, Convergence for weighted sums of \(\tilde \rho\)-mixing random sequences, Math. Appl., 2002, 15(1): 1–4.

    MathSciNet  Google Scholar 

  18. Q. Y. Wu and Y. Y. Jiang, Some strong limit theorems for \(\tilde \rho\)-mixing sequences of random variables, Statistics and Probability Letters, 2008, 78(8): 945–1050.

    Article  MathSciNet  Google Scholar 

  19. Q. Y. Wu and Y. Y. Jiang, Some strong limit theorems for weighted product sums of -mixing sequences of random variables, Journal of Inequalities and Applications, 2009, doi: 10.1155/2009/174-768.

  20. Q. Y. Wu and Y. Y. Jiang, Chover-type laws of the k-iterated logarithm for \(\tilde \rho\)-mixing sequences of random variables, Journal of Mathematical Analysis and Applications, 2010, 366(2): 435–443.

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Peligrad and A. Gut, Almost-sure results for a class of dependent random variables, J. Theoret. Probab., 1999, 12: 87–104.

    Article  MathSciNet  MATH  Google Scholar 

  22. S. X. Gan, Almost sure convergence for \(\tilde \rho\)-mixing random variable sequences, Statist. Probab. Lett., 2004, 67: 289–298.

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Utev and M. Peligrad, Maximal inequalities and an invariance principle for a class of weakly dependent random variables, J. Theoret. Probab., 2003, 16(1): 101–115.

    Article  MathSciNet  MATH  Google Scholar 

  24. Y. H. Wu, Strong consistency and exponential rate of the “minimum L 1-norm” estimates in linear regression models, Computational Statistics and Data Analysis, 1988, 6: 285–295.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Guilin University of Technology, Guilin, 541004, China

    Qunying Wu

Authors
  1. Qunying Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qunying Wu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 11061012, the Support Program of the New Century Guangxi China Ten-hundred-thousand Talents Project under Grant No. 2005214, and the Guangxi, China Science Foundation under Grant No. 0991081.

This paper was recommended for publication by Editor Guohua ZOU.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Q. Further study strong consistency of M estimator in linear model for \(\tilde \rho\)-mixing random samples. J Syst Sci Complex 24, 969–980 (2011). https://doi.org/10.1007/s11424-011-8407-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-8407-7

Key words

Search

Navigation