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

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Author Info
Judith A. Clarke () (Department of Economics, University of Victoria)
Abstract

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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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0701.

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Length: 8 pages
Date of creation: 09 Apr 2007
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Handle: RePEc:vic:vicewp:0701

Note: ISSN 1485-6441
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Related research
Keywords: Logit; Mean squared error; weighted estimaor; linear restrictions;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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  1. 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.
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
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