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Improved Estimation in Measurement Error Models Through Stein Rule Procedure

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  • Shalabh

Abstract

This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression coefficients. A further application may improve the efficiency properties of the estimators of regression coefficients. It is observed that the proposed family of estimators under some constraint on the characterizing scalar dominates the conventional consistent estimator with respect to the criterion of asymptotic risk under a specific quadratic loss function. Then the problem of prediction of the values of the study variable within the sample is considered, and it is found that the predictors based on the proposed family of estimators are always more efficient than the predictors based on the conventional estimator according to asymptotic predictive mean squared error criterion, although both are biased.

Suggested Citation

  • Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:1:p:35-48
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    References listed on IDEAS

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    1. Srivastava, Anil K. & Shalabh, 1997. "A new property of Stein procedure in measurement error model," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 231-234, March.
    2. 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.
    3. R. Friedmann & H. J. Mittag & A. Brandtstater, 1991. "An application of approximate finite sample results to parameter estimation in a linear errors‐in‐variables model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(2), pages 93-106, June.
    4. Guilkey, David K. & Price, J. Michael, 1981. "On comparing restricted least squares estimators," Journal of Econometrics, Elsevier, vol. 15(3), pages 397-404, April.
    5. Zheng, Z., 1986. "On estimation of matrix of normal mean," Journal of Multivariate Analysis, Elsevier, vol. 18(1), pages 70-82, February.
    6. Moran, P. A. P., 1971. "Estimating structural and functional relationships," Journal of Multivariate Analysis, Elsevier, vol. 1(2), pages 232-255, June.
    7. Van Hoa, Tran, 1986. "Improved estimators in some linear errors-in-variables models in finite samples," Economics Letters, Elsevier, vol. 20(4), pages 355-358.
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    Citations

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    Cited by:

    1. 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.
    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.
    3. A. Saleh & B. Kibria, 2013. "Improved ridge regression estimators for the logistic regression model," Computational Statistics, Springer, vol. 28(6), pages 2519-2558, December.
    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. Hayat, Aziz & Bhatti, M. Ishaq, 2013. "Masking of volatility by seasonal adjustment methods," Economic Modelling, Elsevier, vol. 33(C), pages 676-688.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

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