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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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Bibliographic Info

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
Date of revision:
Handle: RePEc:vic:vicewp:0701

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

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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, Econometric Society, vol. 67(3), pages 639-644, May.
  2. 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, American Statistical Association, vol. 96, pages 697-705, June.
  3. Dmitry Danilov, 2005. "Estimation of the mean of a univariate normal distribution when the variance is not known," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 8(3), pages 277-291, December.
  4. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, Elsevier, vol. 122(1), pages 27-46, September.
  5. Giles, Judith A & Giles, David E A, 1993. " Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 145-97, June.
  6. 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, Elsevier, vol. 77(8), pages 803-810, April.
  7. Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 5(1), pages 225-236, June.
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