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Estimation of regression coefficients of interest when other regression coefficients are of no interest: The case of non-normal errors

Author

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  • Zou, Guohua
  • Wan, Alan T.K.
  • Wu, Xiaoyong
  • Chen, Ti

Abstract

This note considers the problem of estimating regression coefficients when some other coefficients in the model are of no interest. For the case of normal errors, Magnus and Durbin [1999. Estimation of regression coefficients of interest when other regression coefficients are of no interest. Econometrica 67, 639-643] and Danilov and Magnus [2004. On the harm that ignoring pretesting can cause. J. Econometrics 122, 27-46] studied this problem and established an equivalence theorem which states that the problem of estimating the coefficients of interest is equivalent to that of finding an optimal estimator of the vector of coefficients of no interest given a single observation from a normal distribution. The aim of this note is to generalize their findings to the large sample non-normal errors case. Some applications of our results are also given.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:77:y:2007:i:8:p:803-810
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Ullah, Aman & Ullah, Shobha, 1978. "Double k-Class Estimators of Coefficients in Linear Regression," Econometrica, Econometric Society, vol. 46(3), pages 705-722, May.
    4. Giles, Judith A., 1991. "Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances," Journal of Econometrics, Elsevier, vol. 50(3), pages 377-398, December.
    5. 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.
    6. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    7. 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. Clarke, Judith A., 2008. "On weighted estimation in linear regression in the presence of parameter uncertainty," Economics Letters, Elsevier, vol. 100(1), pages 1-3, July.
    2. Giuseppe De Luca & Jan R. Magnus & Franco Peracchi, 2017. "Weighted-average least squares estimation of generalized linear models," EIEF Working Papers Series 1711, Einaudi Institute for Economics and Finance (EIEF), revised Aug 2017.
    3. An, Lihua & Nkurunziza, Sévérien & Fung, Karen Y. & Krewski, Daniel & Luginaah, Isaac, 2009. "Shrinkage estimation in general linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2537-2549, May.
    4. repec:eee:econom:v:204:y:2018:i:1:p:1-17 is not listed on IDEAS
    5. 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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