IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i4p726-741.html
   My bibliography  Save this article

Improved estimation in multiple linear regression models with measurement error and general constraint

Author

Listed:
  • Liang, Hua
  • Song, Weixing

Abstract

In this paper, we define two restricted estimators for the regression parameters in a multiple linear regression model with measurement errors when prior information for the parameters is available. We then construct two sets of improved estimators which include the preliminary test estimator, the Stein-type estimator and the positive rule Stein type estimator for both slope and intercept, and examine their statistical properties such as the asymptotic distributional quadratic biases and the asymptotic distributional quadratic risks. We remove the distribution assumption on the error term, which was generally imposed in the literature, but provide a more general investigation of comparison of the quadratic risks for these estimators. Simulation studies illustrate the finite-sample performance of the proposed estimators, which are then used to analyze a dataset from the Nurses Health Study.

Suggested Citation

  • Liang, Hua & Song, Weixing, 2009. "Improved estimation in multiple linear regression models with measurement error and general constraint," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 726-741, April.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:726-741
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00181-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. Schneeweiß, 1976. "Consistent estimation of a regression with errors in the variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 23(1), pages 101-115, December.
    2. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    3. Stanley, T. D., 1986. "Stein-rule least squares estimation : A heuristic for fallible data," Economics Letters, Elsevier, vol. 20(2), pages 147-150.
    4. Kim, H.M. & Saleh, A.K.Md.Ehsanes, 2005. "Improved estimation of regression parameters in measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 273-300, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kim, H.M. & Saleh, A.K.Md.Ehsanes, 2005. "Improved estimation of regression parameters in measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 273-300, August.
    2. Cheng, C.-L. & Shalabh, & Garg, G., 2014. "Coefficient of determination for multiple measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 137-152.
    3. Saleh, A.K.Md. Ehsanes & Shalabh,, 2014. "A ridge regression estimation approach to the measurement error model," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 68-84.
    4. Cheng, C.-L. & Shalabh, & Garg, G., 2016. "Goodness of fit in restricted measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 101-116.
    5. Sukhbir Singh & Kanchan Jain & Suresh Sharma, 2014. "Replicated measurement error model under exact linear restrictions," Statistical Papers, Springer, vol. 55(2), pages 253-274, May.
    6. Shalabh & Garg, Gaurav & Misra, Neeraj, 2009. "Use of prior information in the consistent estimation of regression coefficients in measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1498-1520, August.
    7. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    8. Jain, Kanchan & Singh, Sukhbir & Sharma, Suresh, 2011. "Restricted estimation in multivariate measurement error regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 264-280, February.
    9. T. D. Stanley & Stephen B. Jarrell, 2005. "Meta‐Regression Analysis: A Quantitative Method of Literature Surveys," Journal of Economic Surveys, Wiley Blackwell, vol. 19(3), pages 299-308, July.
    10. Vehkalahti, Kimmo & Puntanen, Simo & Tarkkonen, Lauri, 2007. "Effects of measurement errors in predictor selection of linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1183-1195, October.
    11. T. D. Stanley, 2004. "Does unemployment hysteresis falsify the natural rate hypothesis? a meta‐regression analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 18(4), pages 589-612, September.
    12. A. Saleh & B. Golam Kibria, 2011. "On some ridge regression estimators: a nonparametric approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 819-851.
    13. Thiel, Hendrik & Thomsen, Stephan L., 2013. "Noncognitive skills in economics: Models, measurement, and empirical evidence," Research in Economics, Elsevier, vol. 67(2), pages 189-214.
    14. Hayat, Aziz & Bhatti, M. Ishaq, 2013. "Masking of volatility by seasonal adjustment methods," Economic Modelling, Elsevier, vol. 33(C), pages 676-688.
    15. A. Saleh & Jan Picek & Jan Kalina, 2012. "R-estimation of the parameters of a multiple regression model with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 311-328, April.
    16. Shalabh & Garg, Gaurav & Misra, Neeraj, 2007. "Restricted regression estimation in measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1149-1166, October.
    17. Patriota, Alexandre G. & Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 2011. "A multivariate ultrastructural errors-in-variables model with equation error," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 386-392, February.
    18. A. Ronner & A. Steerneman, 1985. "The occurrence of outliers in the explanatory variable considered in an errors-in-variables framework," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 97-107, December.
    19. R. Ketellapper & A. Ronner, 1984. "Are robust estimation methods useful in the structural errors-in-variables model?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 33-41, December.
    20. T.D. Stanley, 1991. ""Regression-Discontinuity Design" By Any Other Name Might Be Less Problematic," Evaluation Review, , vol. 15(5), pages 605-624, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:726-741. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.