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Improved estimation of regression parameters in measurement error models

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  • Kim, H.M.
  • Saleh, A.K.Md.Ehsanes

Abstract

The problem of simultaneous estimation of the regression parameters in a multiple regression model with measurement errors is considered when it is suspected that the regression parameter vector may be the null-vector with some degree of uncertainty. In this regard, we propose two sets of four estimators, namely, (i) the unrestricted estimator, (ii) the preliminary test estimator, (iii) the Stein-type estimator and (iv) the postive-rule Stein-type estimator. In an asymptotic setup, properties of these estimators are studied based on asymptotic distributional bias, MSE matrices, and risks under a quadratic loss function. In addition to the asymptotic dominance of the Stein-type estimators, the paper contains discussion of dominating confidence sets based on the Stein-type estimation. Asymptotic analysis is considered based on a sequence of local alternatives to obtain the desired results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:95:y:2005:i:2:p:273-300
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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