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Use of prior information in the consistent estimation of regression coefficients in measurement error models

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  • Shalabh
  • Garg, Gaurav
  • Misra, Neeraj
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    Abstract

    A multivariate ultrastructural measurement error model is considered and it is assumed that some prior information is available in the form of exact linear restrictions on regression coefficients. Using the prior information along with the additional knowledge of covariance matrix of measurement errors associated with explanatory vector and reliability matrix, we have proposed three methodologies to construct the consistent estimators which also satisfy the given linear restrictions. Asymptotic distribution of these estimators is derived when measurement errors and random error component are not necessarily normally distributed. Dominance conditions for the superiority of one estimator over the other under the criterion of Löwner ordering are obtained for each case of the additional information. Some conditions are also proposed under which the use of a particular type of information will give a more efficient estimator.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 7 (August)
    Pages: 1498-1520

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1498-1520

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    Related research

    Keywords: Measurement errors Exact linear restriction Ultrastructural model Reliability matrix Löwner ordering;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Geraci, Vincent J, 1977. "Estimation of Simultaneous Equation Models with Measurement Error," Econometrica, Econometric Society, vol. 45(5), pages 1243-55, July.
    2. Srivastava, Anil K. & Shalabh, 1997. "Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal," Journal of Econometrics, Elsevier, vol. 78(2), pages 153-157, June.
    3. Goldberger, Arthur S, 1972. "Maximum-Likelihood Estimation of Regressions Containing Unobservable Independent Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 1-15, February.
    4. Hsiao, Cheng, 1976. "Identification and Estimation of Simultaneous Equation Models with Measurement Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 319-39, June.
    5. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    6. Chi-Lun Cheng & Alexander Kukush, 2006. "Non-Existence of the First Moment of the Adjusted Least Squares Estimator in Multivariate Errors-in-Variables Model," Metrika, Springer, vol. 64(1), pages 41-46, August.
    7. H. Schneeweiß, 1976. "Consistent estimation of a regression with errors in the variables," Metrika, Springer, vol. 23(1), pages 101-115, December.
    8. Geraci, Vincent J, 1983. "Errors in Variables and the Individual Structural Equation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 217-36, February.
    9. Gleser, Leon Jay, 1993. "Estimators of slopes in linear errors-invariables regression models when the predictors have known reliability matrix," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 113-121, May.
    10. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
    11. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    12. Srivastava, Anil K. & Shalabh, 1997. "Consistent estimation for the non-normal ultrastructural model," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 67-73, May.
    13. 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.
    14. Geraci, Vincent J., 1976. "Identification of simultaneous equation models with measurement error," Journal of Econometrics, Elsevier, vol. 4(3), pages 263-283, August.
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    Cited by:
    1. 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.
    2. 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.

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