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Estimating the error variance after a pre-test for an interval restriction on the coefficients

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  • Zhu, Rong
  • Zhou, Sherry Z.F.

Abstract

This paper considers the estimation of the error variance after a pre-test of an interval restriction on the coefficients. We derive the exact finite sample risks of the interval restricted and pre-test estimators of the error variance, and examine the risk properties of the estimators to model misspecification through the omission of relevant regressors. It is found that the pre-test estimator performs better than the interval restricted estimator in terms of the risk properties in a large region of the parameter space; moreover, its risk performance is more robust with respect to the degrees of model misspecification. Furthermore, we propose a bootstrap procedure for estimating the risks of the estimators, to overcome the difficulty of computing the exact risks.

Suggested Citation

  • Zhu, Rong & Zhou, Sherry Z.F., 2011. "Estimating the error variance after a pre-test for an interval restriction on the coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2312-2323, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2312-2323
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    References listed on IDEAS

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    1. Judge, George G. & Yancey, Thomas A., 1981. "Sampling properties of an inequality restricted estimator," Economics Letters, Elsevier, vol. 7(4), pages 327-333.
    2. Ohtani, Kazuhiro, 1988. "Optimal levels of significance of a pre-test in estimating the disturbance variance after the pre-test for a linear hypothesis on coefficients in a linear regression," Economics Letters, Elsevier, vol. 28(2), pages 151-156.
    3. Wan, Alan T. K., 1994. "Risk comparison of the inequality constrained least squares and other related estimators under balanced loss," Economics Letters, Elsevier, vol. 46(3), pages 203-210, November.
    4. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    5. Alan T.K. Wan & Guohua Zou & Kazuhiro Ohtani, 2006. "Further results on optimal critical values of pre-test when estimating the regression error variance," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 159-176, March.
    6. Wan, Alan T. K. & Zou, Guohua, 2003. "Optimal critical values of pre-tests when estimating the regression error variance: analytical findings under a general loss structure," Journal of Econometrics, Elsevier, vol. 114(1), pages 165-196, May.
    7. Clarke, Judith A. & Giles, David E. A. & Wallace, T. Dudley, 1987. "Preliminary-Test Estimation of the Error Variance in Linear Regression," Econometric Theory, Cambridge University Press, vol. 3(02), pages 299-304, April.
    8. Ohtani, Kazuhiro, 1987. "The MSE of the least squares estimator over an interval constraint," Economics Letters, Elsevier, vol. 25(4), pages 351-354.
    9. Clarke, Judith A. & Giles, David E. A. & Wallace, T. Dudley, 1987. "Estimating the error variance in regression after a preliminary test of restrictions on the coefficients," Journal of Econometrics, Elsevier, vol. 34(3), pages 293-304, March.
    10. Escobar, Luis A. & Skarpness, Bradley, 1986. "The bias of the least squares estimator over interval constraints," Economics Letters, Elsevier, vol. 20(4), pages 331-335.
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    Cited by:

    1. Hu, Guikai & Yu, Shenghua & Luo, Han, 2015. "Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 266-276.

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