IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i7p2312-2323.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(11)00038-7
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Ohtani, Kazuhiro, 1987. "The MSE of the least squares estimator over an interval constraint," Economics Letters, Elsevier, vol. 25(4), pages 351-354.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ohtani, Kazuhiro, 2002. "Exact distribution of a pre-test estimator for regression error variance when there are omitted variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 129-140, November.
    3. Qin, Huaizhen & Ouyang, Weiwei, 2016. "Asymmetric risk of the Stein variance estimator under a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 94-100.
    4. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.
    5. Jan R. Magnus & Wendun Wang & Xinyu Zhang, 2016. "Weighted-Average Least Squares Prediction," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1040-1074, June.
    6. Ohtani, Kazuhiro, 1996. "Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 191-199, September.
    7. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    8. Sebastian M. Blanc & Thomas Setzer, 2020. "Bias–Variance Trade-Off and Shrinkage of Weights in Forecast Combination," Management Science, INFORMS, vol. 66(12), pages 5720-5737, December.
    9. Kazuhiro Ohtani & Alan Wan, 2002. "ON THE USE OF THE STEIN VARIANCE ESTIMATOR IN THE DOUBLE k-CLASS ESTIMATOR IN REGRESSION," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 121-134.
    10. Buatikan Mirezi & Selahattin Kaçıranlar, 2023. "Admissible linear estimators in the general Gauss–Markov model under generalized extended balanced loss function," Statistical Papers, Springer, vol. 64(1), pages 73-92, February.
    11. Dorfman, Jeffrey H. & McIntosh, Christopher S., 2001. "Imposing inequality restrictions: efficiency gains from economic theory," Economics Letters, Elsevier, vol. 71(2), pages 205-209, May.
    12. Davy Paindaveine & Joséa Rasoafaraniaina & Thomas Verdebout, 2021. "Preliminary test estimation in uniformly locally asymptotically normal models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 689-707, June.
    13. Ohtani, Kazuhiro, 1998. "Inadmissibility of the Stein-rule estimator under the balanced loss function," Journal of Econometrics, Elsevier, vol. 88(1), pages 193-201, November.
    14. Ulrike Grömping & Sabine Landau, 2010. "Do not adjust coefficients in Shapley value regression," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 194-202, March.
    15. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.
    16. Wang, W., 2013. "Essays on model averaging and political economics," Other publications TiSEM 2e45376b-749e-4464-aba7-f, Tilburg University, School of Economics and Management.
    17. Chaturvedi, Anoop & Shalabh, 2004. "Risk and Pitman closeness properties of feasible generalized double k-class estimators in linear regression models with non-spherical disturbances under balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 229-256, August.
    18. Paul Knottnerus, 2016. "On new variance approximations for linear models with inequality constraints," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 26-46, February.
    19. Helen X. H. Bao & Alan T. K. Wan, 2007. "Improved Estimators of Hedonic Housing Price Models," Journal of Real Estate Research, American Real Estate Society, vol. 29(3), pages 267-302.
    20. Magnus, J.R. & Wang, W. & Zhang, Xinyu, 2012. "WALS Prediction," Other publications TiSEM 7715e942-b446-4985-8216-f, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2312-2323. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.