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On Weighted Estimation in Linear Regression in th Presence of Parameter Uncertainty

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We consider estimating the linear regression model’s coefficients when there is uncertainty about coefficient restrictions. Theorems establish that the mean squared errors of combination estimators, formed as weighted averages of the ordinary least squares and one or more restricted least squares estimators, depend on finding the optimal estimator of a single normally distributed vector. Our results generalize those of Magnus and Durbin (1999) [Magnus, J.R., Durbin, J. 1999. Estimation of regression coefficients of interest when other regression coefficients are of no interest. Econometrica 67, 639-643] and Danilov and Magnus (2004) [Danilov, D., Magnus, J.R. 2004. On the harm that ignoring pretesting can cause. Journal of Econometrics 122, 27-46].

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  • Judith A. Clarke, 2007. "On Weighted Estimation in Linear Regression in th Presence of Parameter Uncertainty," Econometrics Working Papers 0701, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0701
    Note: ISSN 1485-6441
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    1. Kim, Tae-Hwan & White, Halbert, 1999. "James-Stein Type Estimators in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt9914w10r, Department of Economics, UC San Diego.
    2. Dmitry Danilov, 2005. "Estimation of the mean of a univariate normal distribution when the variance is not known," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 277-291, December.
    3. Kim, Tae-Hwan & White, Halbert, 2000. "James-Stein Type Estimators in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt4zq9k3qh, Department of Economics, UC San Diego.
    4. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    5. Giles, Judith A & Giles, David E A, 1993. "Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 7(2), pages 145-197, June.
    6. Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 225-236, June.
    7. Kim, Tae-Hwan & White, Halbert, 2000. "James-Stein Type Estimator in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt3mn102zs, Department of Economics, UC San Diego.
    8. Zou, Guohua & Wan, Alan T.K. & Wu, Xiaoyong & Chen, Ti, 2007. "Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 803-810, April.
    9. Kim T-H. & White H., 2001. "James-Stein-Type Estimators in Large Samples With Application to the Least Absolute Deviations Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 697-705, June.
    10. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
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    Cited by:

    1. Judith Anne Clarke, 2017. "Model Averaging OLS and 2SLS: An Application of the WALS Procedure," Econometrics Working Papers 1701, Department of Economics, University of Victoria.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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