Skip to main content
Log in

Corrected-loss estimation for Error-in-Variable partially linear model

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.

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

Access this article

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. Anderson T W. Estimating linear statistical relationship. Ann Statist, 1984, 12: 1–45

    Article  MATH  MathSciNet  Google Scholar 

  2. Carroll R J, Hall P. Lower-order approximations in deconvolution and regression with errors in variables. J Roy Statist Soc Ser B, 2004, 66: 31–46

    Article  MATH  MathSciNet  Google Scholar 

  3. Carroll R J, Maca J D, Ruppert D. Nonparametric regression in the presence of measurement error. Biometrika, 1999, 86: 541–554

    Article  MATH  MathSciNet  Google Scholar 

  4. Carroll R J, Ruppert D, Stefanski L A, et al. Measurement Error in Nonlinear Models: A Modern Perspective. 2nd ed. London: CRC Press, 2006

    Book  Google Scholar 

  5. Cheng C L, Van Ness J W. Statistical Regression with Measurement Error. London: Arnold, 1999

    MATH  Google Scholar 

  6. Cheng C L, Van Ness J W. Generalized M-estimators for errors-in-variables regression. Ann Statist, 1992, 20: 385–397

    Article  MATH  MathSciNet  Google Scholar 

  7. Cui H J. Asymptotic normality of M-estimates in the EV model. J Syst Sci Math, 1997, 3: 225–236

    Google Scholar 

  8. Cui H J. Asymptotic properties of generalized MAD estimators in EV model. Sci China Ser A, 1997, 2: 119–131

    Google Scholar 

  9. Cui H J. Estimation in partial linear EV models with replicated observations. Sci China Ser A, 2004, 47: 144–159

    Article  MATH  MathSciNet  Google Scholar 

  10. Delaigle A, Meister A. Nonparametric regression estimation in the heteroscedastic errors-in-variables problem. J Amer Statist Assoc, 2007, 102: 1416–1426

    Article  MATH  MathSciNet  Google Scholar 

  11. Engle R F, Granger C W J, Rice J, et al. Semiparametric estimates of the relation between weather and electricity sales. J Amer Statist Assoc, 1986, 81: 310–320

    Article  Google Scholar 

  12. Fan J, Huang T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli, 2005, 11: 1031–1057

    Article  MATH  MathSciNet  Google Scholar 

  13. Fan J, Truong Y K. Nonparametric regression with errors in variables. Ann Statist, 1993, 21: 1900–1925

    Article  MATH  MathSciNet  Google Scholar 

  14. Fuller W A. Measurement Error Model. New York: John Wiley, 1987

    Book  Google Scholar 

  15. Gleser L J. Improvement of the naive approach to estimation in nonlinear error-in-variables regression models. Comtemp Math, 1990, 112: 99–120

    MathSciNet  Google Scholar 

  16. He X, Liang H. Quantile regression estimates for a class of linear and partially linear errors-in-variables models. Statist Sinica, 2000, 10: 129–140

    MATH  MathSciNet  Google Scholar 

  17. Hu T, Cui H J. t-Type estimators for a class of linear errors-in-variables models. Statist Sinica, 2009, 19: 1013–1036

    MATH  MathSciNet  Google Scholar 

  18. Kannel W B, Newton J D, Wentworth D, et al. Overall and coronary heart disease mortality rates in relation to major risk factors in 325, 348 men screened for MRFIT. American Heart J, 1986, 112: 825–836

    Article  Google Scholar 

  19. Liang H, Härdle W, Carroll R J. Estimation in a semiparametric partially linear errors-in-variables model. Ann Statist, 1999, 27: 1519–1535

    Article  MATH  MathSciNet  Google Scholar 

  20. Liang H, Li R. Variable selection for partially linear models with measurement errors. J Amer Statist Assoc, 2009, 104: 234–248

    Article  MathSciNet  Google Scholar 

  21. Stefanski L A. Measurement error models. J Amer Statist Assoc, 2000, 95: 1353–1358

    Article  MATH  MathSciNet  Google Scholar 

  22. Stefanski L A, Cook R J. Simulation-extrapolation: The measurement error jackknife. J Amer Statist Assoc, 1995, 90: 1247–1256

    Article  MATH  MathSciNet  Google Scholar 

  23. Tong X W, Cui H J, Yu F P. Consistency and normality of Huber-Dutter estimators for partial linear model. Sci China Ser A, 2008, 51: 1831–1842

    Article  MATH  MathSciNet  Google Scholar 

  24. Wang H, Stefanski L, Zhu Z. Corrected-loss estimation for quantile regression with covariate measurement error. Biometrika, 2012, 99: 405–421

    Article  MATH  MathSciNet  Google Scholar 

  25. Wang Q H. Estimation of partial linear errors-in-variables models with censored data. Comm Stat Th Meth, 1999, 30: 41–54

    Article  Google Scholar 

  26. Wang Q H. Nonparametric regression function estimation with surrogate data and validation sampling. J Multivariate Anal, 2006, 97: 1142–1161

    Article  MATH  MathSciNet  Google Scholar 

  27. Wang Q H, Zhu L X. Estimation in partly linear errors-in-variables models with validation data. J Multivariate Anal, 2001, 69: 30–64

    Article  Google Scholar 

  28. Zamar R H. Robust estimation in the error-in-variable model. Biometrika, 1989, 76: 149–160

    Article  MATH  MathSciNet  Google Scholar 

  29. Zhu L P, Li R Z, Cui H J. Robust estimation for partially linear models with large-dimensional covariates. Sci China Math, 2013, 56: 2069–2088

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to XingWei Tong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, J., Tong, X. Corrected-loss estimation for Error-in-Variable partially linear model. Sci. China Math. 58, 1101–1114 (2015). https://doi.org/10.1007/s11425-015-4980-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-015-4980-x

Keywords

MSC(2010)

Navigation